GIFT  OF 


X.  cl    A 


A  SHIP  ILLUSTRATING  THE  "DAZZLE"  SYSTEM  OF  CAMOUFLAGE 

The  pictures  show  the  same  ship,  headed  in  the  same  direction,  but  at  three  dif- 
ferent distances.  When  seen  at  a  great  distance,  especially  through  the  periscope 
of  a  submarine,  the  ship  appears  to  be  headed  in  a  direction  quite  different  from i  its 
actual  course,  because  of  the  false-perspective  design  painted  on  it  (bee  page  4bl.) 


ESSENTIALS  OF  PHYSICS 


BY 

GEORGE  A.  HOADLEY,  C.E.,  Sc.D. 

PROFESSOR    OF    PHYSICS    IN   SWARTHMORE 
COLLEGE 


REVISED  EDITION 


AMERICAN  BOOK  COMPANY 

NEW  YORK  CINCINNATI  CHICAGO 

BOSTON  ATLANTA 


^ 


COPYBIOHT,  1918,  IN  GREAT  BRITAIN. 

COPYRIGHT,  1921,  BY 
•AMERICAN  BOOK  COMPANY. 


E88BN.   OF   PUTS.  REV. 
W.   P.   1 


PREFACE 

THE  most  essential  'thing  in  the  study  of  any  science 
is  that  there  should  be  a  thorough  understanding  of  the 
fundamental  principles  upon  which  it  is  based.  In  this 
text  experimental  demonstrations  are  used  to  show  the 
relation  between  the  conditions  imposed  and  the  results 
obtained.  These  demonstrations  lead  to  the  statements 
of  fundamental  principles  which  are  here  given  either  as 
simple  formulas  or  as  expressions  of  these  formulas  in 
ordinary  language. 

It  has  also  come  to  be  generally  understood  that  there 
is  no  branch  of  natural  science  that  has  a  more  direct 
application  to  the  needs  of  modern  life  than  Physics.  It 
is  for  this  reason  that  emphasis  is  placed  in  this  book 
upon  the  things  that  are  essential  in  understanding  the 
applications  of  the  principles  of  Physics  to  that  which  is 
a  part  of  our  everyday  experience.  At  -the  end  of  each 
section  there  is  a  group  of  questions,  which  not  only  serve 
to  recall  the  principles  considered  in  the  section  and  to 
stimulate  the  interest  of  the  pupil,  but  also  suggest  direc- 
tions in  which  these  principles  can  be  applied.  Moreover, 
the  problems  that  are  given  are  practical  problems  based 
on  conditions  that  are  to  be  met  with  constantly. 

The  general  applications  of  Physics  to  the  doing  of 
things  are  graphically  presented  throughout  by  a  series 
of  full-page  illustrations.  Some  of  these  show  the  advances 
that  have  been  made  in  well-known  machines ;  as  an 
example,  the  modern  locomotive  compared  with  Steven- 

3 

462299 


4  PREFACE 

• 

son's  Rocket.  Automobiles,  airships,  the  submarine,  and  the 
electric  railroad  train  exemplify  the  most  recent  methods  of 
applying  gasoline  and  electricity  as  motive  powej^thile  the 
dirigible  and  the  airplane  are  examples  of  wha^Bls  been 
done  to  secure  a  means  of  traveling  through  the  most  un- 
stable of  fluids,  the  air.  The  locks  of  the  Panama  Canal  are 
triumphs  of  mechanical  engineering.  The  work  of  the  elec- 
trical engineer  is  shown  in  the  electric  power  stations  and  the 
electric  train.  The  development  of  the  audion  has  made  it 
possible  to  hold  telephone  conversations  for  almost  unlim- 
ited distances;  and  by  the  teleostereograph  one  may  trans- 
mit photographs  long  distances  by  wire  in  a  few  minutes. 
The  non-magnetic  ship,  the  Carnegie,  is  shown  as  an  exam- 
ple of  how  the  scientific  study  of  magnetic  phenomena  can 
be  made  to  serve  the  navigator.  The  illustration  of  the  mov- 
ing picture  studio  indicates  how  the  exacting  requirements 
for  lighting  are  met.  Another  recent  application  of  the  prin- 
ciples controlling  light  is  seen  in  the  camouflage  illustrated 
in  the  frontispiece. 

Nearly  all  engineering  is  applied  physics  and  hence  has  a 
place  in  the  treatment  of  the  subject. 

The  hope  is  expressed  that  those  who  study  the  essential 
principles  of  Physics,  as  treated  in  this  book,  will  master 
them  so  thoroughly  that  they  will  take  pleasure  in  tracing 
the  dependence  of  our  way  of  living  upon  these  underlying 
principles. 

Acknowledgment  is  made  of  many  helpful  suggestions 
made  by  teachers  of  Physics  and  to  publishers  who  have 
granted  the  use  of  subjects  for  illustration. 

GEORGE  A.   HOADLEY. 

SWARTHMORE    COLLEGE. 


TABLE  OF  CONTENTS 


CHAPTER  PAGB 

J.     INTRODUCTORY .9 

II.     THE  PROPERTIES  OF  MATTER  .         .         .        .         .        .14 

I.     General  Properties           ...,,.  14 

II.     Specific  Properties  .                  22 

III.  THE  MECHANICS  OF  SOLIDS 34 

I.     Motion,  Velocity,  and  Force  .....  34 

II.     Energy  and  Work 70 

III.  Gravitation  and  Gravity         .....  80 

IV.  The  Pendulum 89 

V.     Machines 96 

IV.  LIQUIDS 119 

I.     Molecular  Forces  in  Liquids  .         .         .         .         .119 

IT.     The  Mechanics  of  Liquids      .....  129 

ITT.     Specific  Gravity       .         .         ...        .         .146 

V.     GASES.         .                          157 

VI.     SOUND 191 

T.     Wave  Motion  and  Velocity    .         .         .         .        .  191 
IT.     Interference,  Resonance,  and  Music        .         .         .  203 
ITT.     Vibration  of  Strings,  Air  Columns,  etc.;  Combi- 
nation of  Vibrations    .                 .         .         .         .  221 

VTI.     HEAT 237 

I.     Temperature  and  its  Measurement         .         .         .  237 

IT.     Production  and  Transmission  of  Heat  .         .         .  246 

III.  Expansion,  Fusion,  and  Vaporization    .         .         .  259 

IV.  Calorimetry 281 

V.     Heat  and  Work      .......  287 

5 


6  TABLE  OF  CONTENTS 

CHAPTER  PAOK 

VIII.     MAGNETISM 300 

IX.     ELECTRICITY     .         . 318 

I.     Static  Electricity 318 

II.     Current  Electricity        .         .         .         .         .         .  346 

III.  The  Effects  of  the  Current 362 

IV.  Electrical  Measurements 380 

V.     Induced  Currents  and  the  Dynamo      .         .         .  393 

VT.     Commercial  Applications  of  Electricity       .         .  417 

X.     LIGHT         .         . 435 

I.     Nature  and  Intensity  of  Light      ....  435 
If.     The  Reflection  of  Light        .         .        .         .         .443 

III.  The  Refraction  of  Light 457 

IV.  Dispersion  and  Polarization          ....  473 
V.     Optical  Instruments      .         .         .        .        .        .491 

XI.     INVISIBLE  RADIATIONS 506 

ANSWERS  TO  NUMERICAL  PROBLEMS 519 

TABLE  OF  CONVERSION  FACTORS 522 

FORMULAS 524 

DEFINITIONS           .        .        .        ...         .        .        .        .  526 

SUPPLEMENTARY  QUESTIONS  AND  PROBLEMS          .         .         .         .531 

INDEX  535 


FULL-PAGE   ILLUSTRATIONS 

The  "  Dazzle "  System  of  Camouflage         .       .       .      Frontispiece 

PAGE 

Tne  British  Dirigible  R  34 .  8 

Ice' Crystals.     Frost  on  a  Window       .        .        .        .        .        .26 

Automobile  Race 35 

A  Parachute  in  Action   .        .       .......  41 

Loading  a  Railroad  Car  on  a  Ship       ......  75 

Fixed  and  Movable  Pulleys  in  Use 107 

A  Submarine;  Exterior  and  Interior 137 

Dynamos  Run  by  Turbines  at  Niagara  Falls     ....  142 

A  Lock  in  the  Panama  Canal 145 

Diagram  of  a  Gas  Supply  System        .       .       .       .       .       .  164 

The  American  Seaplane  NC  4      .......  169 

Photographs  of  Cylindrical  Sound  Waves 208 

A  Modern  Locomotive 293 

Automobile  Engine  and  Transmission        .       .       .       .        .  297 

Automobile  Carburetor,  Rear  Axle,  etc 298 

The  Non-Magnetic  Ship  Carnegie  with  Instruments        .        .312 

Turbo-Generator  of  the  Philadelphia  Electric  Company         .  424 

Electric  Locomotive  and  Transcontinental  Passenger  Train  .  430 

Compound  Microscope  and  Other  Apparatus    ....  493 

Photographic  Negative  and  Print 498 

Moving  Picture  Studio,  with  Camera,  etc 501 

Teleostereograph  Transmitter,  with  a  Photograph  Sent  by 

Wire  502 


Il 


B 

I! 


8  1 


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ESSENTIALS   OF   PHYSICS 


CHAPTER  I 

INTRODUCTORY 

WHEN  we  begin  the  study  of  physics  in  school,  we  already 
have  a  certain  amount  of  information  concerning  physical 
phenomena.  We  know,  for  instance,  that  water  can  be 
changed  into  ice  or  into  steam ;  we  have  seen  the  colors  of 
the  rainbow;  we  know  that  an  unsupported  body  will  fall. 
It  is  the  purpose  of  the  study  of  physics  to  add  to  this  infor- 
mation and  to  put  our  knowledge  into  orderly  arrangement. 

1.  Physical  and  Chemical  Changes.  —  The  physical  phe- 
nomena, the  laws  of  which  we  are  to  investigate,  are  the 
phenomena  of  matter  and  energy  which  may  occur  with- 
out changing  the  identity  of  a  substance.  These  phenom- 
ena are  caused  by  various  physical  forces,  and  include  very 
many  physical  changes.  Whenever  a  change  takes  place 
in  matter  without  destroying  the  identity  of  the  substance, 
it  is  known  as  a  physical  change.  The  fall  of  a  stone  thrown 
into  the  air,  the  changing  of  water  into  steam,  the  shrinking 
of  a  board  while  seasoning,  the  attraction  between  a  magnet 
and  a  nail,  are  all  physical  phenomena,  and  the  changes  that 
take  place  are  physical  changes.  If,  however,  the  board  is 
burned,  or  .the  nail  is  eaten  by  acids,  the  identity  of  the  sub- 
stance is  destroyed,  and  the  change  is  a  chemical  change. 

9 


tO .  INTRODUCTORY 

2.  Matter  is  that  which  occupies  space  and  may  be  per- 
ceived by  one  or  more  of  the  senses.     There  are  various 
kinds  of  matter,  called  substances,  such  as  wood,  stone, 
water,  air,  etc.,  while  bodies  are  composed  of  definite  vol- 
umes of  these  substances. 

3.  Atoms  and  Molecules.  —  The  fact  that  bodies  can  be 
compressed  gave  rise  to  the  belief  that  the  space  they  oc- 
cupy is  not  filled  entirely  by  the  matter  of  which  they  are 
composed,  and  that  its  particles  do  not  really  touch  one 
another.     These    particles  are    called  molecules,   and  they 
are  the  smallest  parts  into  which  a  body  can  be  divided 
without  destroying  the  substance  as   such.     If  the  forces 
which  keep  the  molecule  intact  are  overcome,  the  mole- 
cule may  be  broken  up  into  atoms,  which  are  understood 
to  be  the  smallest  quantities  of  matter  that  can  enter  into 
combination.     The  name  electron  has  been  given  to  particles 
of  matter  smaller  than  the  atom,  which  act  as  carriers  of  nega- 
tive electricity. 

£.  Size  of  Molecules.  —  Molecules  are  so  small  that  they 
cannot  be  seen  by  microscopes  of  the  highest  power.  Lord 
Kelvin  (Sir  William  Thomson),  however,  calculated  their 
size  in  some  substances,  and  from  a  study  of  the  thickness  of 
the  film  in  soap  bubbles  he  found  that  if  a  globe  of  water 
the  size  of  a  football  were  magnified  to  the  size  of  the  earth, 
the  molecules  would  occupy  spaces  intermediate  in  size 
between  small  shot  and  footballs. 

5.  States  of  Matter.  —  In  the  air  we  breathe,  the  water 
we  drink,  and  the  bread  we  eat  we  have  examples  of  the 
three  different  forms  or  states  that  matter  can  assume; 
namely,  gaseous,  liquid,  and  solid.  A  solid  is  a  body  which, 


KINETIC  THEORY  OF  MATTER  11 

at  ordinary  temperatures  and  under  slight  pressures,  does 
not  change  its  shape.  If  the  shape  is  changed  under  these 
conditions,  the  body  is  a  fluid.  Fluids  may  be  divided 
into  two  classes.  Those  that  retain  a  definite  surface  on 
being  poured  into  a  vessel  are  liquids,  while  those  that 
have  a  tendency  to  expand  indefinitely  are  gases. 

Bodies  form  an  almost  continuous  gradation  from  the  most  rigid 
solid  to  the  most  tenuous  gas,  and  the  above  classification  may  be 
extended  as  in  the  following  table : 

Rigid  solid .  Steel 

Soft  solid Putty 

Viscous  liquid      . Tar 

Mobile  liquid Water 

Liquid  in  minute  separate  particles  mixed  with  gas    .  Fog  or  cloud 

Gas Air 

Fluids  flow ;  it  is  commonly  supposed  that  solids  never 
do.  This  is  not  strictly  true,  since  it  has  been  shown  that 
under  certain  pressures  solid  bodies  also  flow.  The  state 
of  matter  is  largely  determined  by  conditions  of  temperature 
and  pressure.  A  stick  of  sealing  wax  fastened  at  one  end 
so  that  it  will  stand  horizontally  and  having  a  two-pound 
weight  attached  to  the  other  end  will  become  permanently 
bent  in  a  short  time;  an  asphalt  pavement  on  a  sloping 
street  will  flow  down  hill  during  a  hot  day ;  and  a  bullet 
placed  upon  a  cake  of  shoemaker's  wax,  resting  upon  two 
corks  in  a  dish  of  water,  will  in  a  few  months  pass  entirely 
through  the  wax,  while  the  corks  will  pass  upward  into  it. 
All  these  are  examples  of  what  are  called  solid  bodies,  yet 
under  the  proper  conditions  they  are  seen  to  flow. 

6.  Kinetic  Theory  of  Matter.  —  According  to  the  kinetic 
theory  of  the  structure  of  matter,  the  molecules  of  all  bodies 


12  INTRODUCTORY 

are  in  rapid  vibration  and  the  three  states  which  matter  as- 
sumes may  be  considered  as  resulting  from  the  kind  of  mo- 
tion of  the  molecules  and  their  relative  velocities. 

In  solids  the  motion  of  the  molecule  is  restricted  to  a  lim- 
ited space,  and  although  it  is  in  constant  vibration,  its  posi- 
tion with  respect  to  the  other  molecules  of  the  body  is  rela- 
tively fixed.  Hence  the  shape  of  a  rigid  solid,  under  normal 
conditions  of  pressure  and  temperature,  is  unchanged. 

In  liquids  the  molecule  is  free  to  move  in  any  direction. 
This  means  that  the  molecules  of  a  liquid  will  glide  over 
one  another,  and  that  the  liquid  will  take  the  shape  of  any 
vessel  into  which  it  is  poured. 

In  gases  the  molecule  has  a  high  velocity,  moving  in  a 
straight-line  path  until  it  comes  in  contact  with  some  other 
molecule  or  with  the  walls  of  the  containing  vessel.  On 
account  of  this  high  molecular  velocity  a  gas  cannot  be  kept 
in  an  open  vessel,  and  however  small  the  quantity  of  gas, 
it  will  always  fill  any  vessel  in  which  it  is  confined.  The 
quantity  of  gas  in  a  closed  vessel  determines  the  pressure  it 
will  exert  upon  the  walls. 

Some  substances  assume  all  three  states  through  a  change 
of  temperature  alone,  as  water,  which  may  be  solid  (ice), 
liquid  (water)  and  gaseous  (invisible  vapor).  Others  re- 
quire a  change  of  pressure  as  well  as  a  change  of  temperature. 

7.  Experiments.  —  An  experiment  is  a  question  put  to 
nature,  and  the  results  obtained  by  it  are  her  answer.  If 
the  conditions  are  the  same,  it  is  found  that  to  a  given  ques- 
tion nature  always  makes  the  same  answer,  and  thus  we  learn 
that  the  order  of  nature  is  constant;  or  that  she  has  definite 
laws  by  which  she  works.  A  careful  study  of  the  experiments 
described  in  the  text  for  class  demonstrations,  attended  by 


PHYSICS  13 

practical  work  in  the  laboratory,  will  show  the  student  in 
how  great  variety  the  questions  can  be  asked,  and  will  show 
that  every  changed  condition  has  its  own  effect. 

It  is  by  means  of  experiments  that  physicists  have  dis- 
covered the  laws  of  physics.  In  interpreting  the  results 
of  various  experiments  an  hypothesis  is  formed  to  explain 
these  results.  When  the  hypothesis  is  found  to  account  satis- 
factorily for  all  the  observed  facts,  it  becomes  an  accepted 
theory;  when  this  theory  is  established  so  firmly  that  it 
cannot  be  overthrown,  it  is  the  expression  of  physical  law. 

8.  Physics  is  that  science  of  matter  and  energy  which  treats 
of  the  laws  that  express  the  relation  between  physical  phe~ 
nomena  and  their  causes.  In  order  to  study  and  verify  these 
laws  the  student  makes  use  of  experiments  in  which  various 
changes  in  the  conditions  may  be  made  and  their  results 
noted. 


CHAPTER   II 


THE  PROPERTIES   OF   MATTER 

9.  General  and  Specific  Properties.  —  In  considering 
the  properties  of  matter  a  distinction  should  be  made  be- 
tween those  properties  that  belong  to  matter  itself  and  those 
that  belong  to  bodies  only. 

General  properties  are  those  found  in  all  matter,  such  as 
extension,  division,  impenetrability,  porosity,  inertia. 

Specific  properties  are  those  found  in  certain  kinds  of  matter 
only,  such  as  ductility,  hardness,  malleability. 

I.     GENERAL  PROPERTIES 

10.  Impenetrability.  —  Space  that  is  occupied 
by  one  portion  of  matter  cannot  at  the  same 
time  be  occupied  by  any  other  portion.  This  is 
a  property  of  matter  rather  than  of  bodies. 

Demonstration.  —  Push  the  closed  end  of  a  test  tube 
into  the  water  in  a  graduate  that  is  partly  full,  as 
shown  in  Fig.  1.  The  difference  between  the  readings 
of  the  water  surface  before  and  after  the  tube  is  in- 
serted will  give  the  volume  of  the  submerged  part  of 
the  tube,  which  is  the  same  as  that  of  the  displaced 
water. 

Fia  x  A  nail  driven  into  a  block  of  wood  pierces  the 

block  and  pushes  the  substance  of  the  wood  to- 
gether. The  block  is  usually  not  increased  in  size,  but  the 
wood  now  occupies  only  part  of  the  space  it  originally 
occupied. 

14 


GENERAL  PROPERTIES 


15 


11.  Porosity.  —  A  body  is  said  to  be  porous,  or  to  have 
porosity,  because  the  particles  of  matter  of  which  it  is  com- 
posed do  not  fill  the  entire  volume  occupied  by  it.  The 
pores  in  bodies  vary  in  size  from  those  that  can  be  seen  in  a 
sponge  or  a  piece  of  charcoal,  to  those  in  stone  or  metal, 
which  may  be  invisible  even  though  a  microscope  of  the 
highest  power  be  used.  All  bodies  are  porous. 

The  fact  that  a  blotter  will  absorb  ink  and  that  a  drop  of 
oil  will  pass  into  a  fine-grained  piece  of  polished  marble 
depends  upon  the  porosity  of  the  blotter  and  the  marble. 

Demonstrations.  —  The  porosity  of  leather  may  be  proved  by  the 
use  of  the  apparatus  shown  in  Fig.  2.  The  funnel  A  has  a  long  stem 
over  the  end  of  which  there  is  securely  tied  a 
piece  of  stretched  wash  leather  B.  Pour  mer- 
cury into  the  funnel,  and  it  will  pass  through 
the  pores  in  the  leather  and  fall  in  the  form  of 
a  fine  rain  into  the  jar  below.  As  the  mercury 
is  thus  freed  from  all  mechanical  impurities, 
the  process  is  of  practical  value. 

Pour  water  into  a  glass  tube  about  a  meter 
long,  until  it  is  nearly  half  full,  and  then  add 
colored  alcohol  until  the  surface  is  a  half  inch 
from  the  end  of  the  tube.  If  this  is  done  care- 
fully, the  line  of  division  between  the  water  and 
the  alcohol  can  be  clearly  seen.  Now  place 
the  finger  over  the  end  of  the  tube  and  invert 
it.  The  water  will  be  seen  to  flow  down 
through  the  lighter  alcohol,  and  minute  bubbles 
of  air  will  rise  through  the  mixed  liquid. 
Invert  the  tube  two  or  three  times,  and  the 
length  of  the  liquid  column  will  be  half  an  'inch  or  more  less  than 
before.  What  does  this  demonstration  teach? 

The  existence  of  spaces  that  are  not  occupied  by  the 
molecules  of  a  liquid  can  be  illustrated  by  filling  three  glasses, 


FIG.  2 


16  THE  PROPERTIES  OF  MATTER 

one  with  smooth  round  peas,  one  with  fine  shot,  and  one  with 
water.  Let  the  first  be  level  full,  then  pour  shot  upon  the 
peas  and  shake  down,  being  careful  that  the  surface  of  the 
peas  is  not  raised.  When  no  more  shot  can  be  put  in,  pour 
in  water  until  it  comes  to  the  top  of  the  peas. 

12.  Compressibility.  —  Since  the  volume  of  a  body  can 
be  reduced  by  pressure,  bodies  are  said  to  be  compressible. 
This    property   depends    upon    porosity.     Gases    are    very 
compressible,  solids  to  a  much  less  degree,  and  liquids  are 
almost  incompressible. 

By  doubling  the  pressure  upon  a  gas  its  volume  is  dimin- 
ished one  half,  while  changing  the  pressure  upon  water  from 
15  Ib.  per  square  inch  to  30  Ib.  per  square  inch  diminishes  its 
volume  only  aTWo  • 

13.  Indestructibility.  —  Matter  can  be  made  to  assume 
different  forms  as  the  result  of  physical  changes,  and  it  can 
be  combined  with  other  matter,  or  broken  up  into  different 
kinds  of  matter,  through  chemical  forces ;    but  matter  itself 
cannot  be  destroyed. 

The  disappearance  of  visible  matter  in  the  boiling  away 
of  water  is  only  a  change  from  the  liquid  to  the  vaporous 
condition. 

If,  after  burning  a  piece  of  coal,  all  the  products  of  the 
combustion  (both  solids  and  gases)  are  carefully  weighed, 
it  is  found  that  the  sum  of  their  weights  is  the  same  as  the 
weight  of  the  coal  and  the  oxygen  used  up  in  the  combustion. 

14.  Divisibility.  — -  Bodies    can   be    divided   into    smaller 
parts  without  changing  the  matter  composing  them.     Di- 
visibility by  mechanical  means   has   practically  no  limit. 
The  finest  crayon  dust  is  made  up  of  small  bodies  of  chalk, 
as  may  be  seen  by  examining  it  with  a  microscope. 


GENERAL  PROPERTIES  17 

Demonstration.  —  Drop  a  little  red  ink  upon  the  surface  of  water 
in  a  beaker.  It  will  mix  gradually,  and  a  thread  of  colored  water 
will  pass  slowly  downward.  Let  the  beaker  stand  undisturbed  for  a 
few  days,  and  the  ink  will  be  distributed  uniformly  throughout  the 
water.  Its  finely  divided  state  is  shown  by  the  fact  that  every 
drop  of  the  solution  is  visibly  colored. 

15.  Inertia  is  the  tendency  a  body  has  to  retain  its  con- 
dition of  rest  or  motion.     Whenever  a  body  is  at  rest,  it 
can  be  put  in  motion  only  by  some  force  outside  of  itself; 
and  whenever  a  body  is  in  motion,  the  rate  or  direction  of 
this  motion  can  be  changed  only  by  the  application  of  a 
force  from  without  the  body.     This  property  is,  therefore, 
purely  negative. 

Demonstration.  —  Place  a  smooth  flat  card  on  the  mouth  of  a 
bottle  with  a  small  neck,  and  on  it  put  a  small  marble  exactly  over 
the  mouth  of  the  bottle.  A  snap  with  the  finger  on  one  corner  of 
the  card  will  send  it  spinning  across  the  room,  while  the  ball  will 
drop  into  the  bottle.  Place  a  little  cotton  inside  the  bottle.  Why? 

Inertia  is  illustrated  in  a  great  many  accidents :  for  example, 
the  spilling  of  a  liquid  in  a  dish  that  is  moved  too  quickly ; 
the  shock  to  a  railway  passenger  when  the  air  brakes  are 
applied  too  suddenly ;  the  fall  caused  by  jumping  from  a 
rapidly  moving  car. 

Use  is  made  of  inertia,  as  in  driving  on  the  head  of  a  mallet 
by  striking  the  end  of  the  handle ;  throwing  an  apple  stuck 
on  the  end  of  a  rod ;  or  changing  the  position  of  a  column 
of  mercury  in  a  glass  tube  by  jerking  the  tube  lengthwise. 

16.  Elasticity.  —  When  a  tennis  ball  is  compressed  into 
smaller  volume  between  the  hands,  it  feels  springy,  or  elastic, 
because  the  contained    air    tends  to   resume   its   original 
volume ;  that  is,  the  molecules  tend  to  regain  their  original 
distance  apart.     All  gases  and  liquids,  and  to  a  certain  ex- 
Rev. 


lg  THE  PROPERTIES  OF  MATTER 

tent  solids  also,  show  a  similar  reaction  against  external 
pressure,  and  are  said  to  have  elasticity  of  volume. 

When  the  shape  of  a  solid  body  is  slightly  changed  by  an 
external  force,  it  usually  tends  to  resume  its  original  form. 
This  elasticity  of  form  may  be  classified  as  follows  (the  corre- 
sponding external  forces  being  given  in  parentheses) : 

(a)  Elasticity  of  Compression  (pressure) ;  it  is  shown,  for 
example,  by  the  rebound  of  a  solid  rubber  ball  dropped  upon 
the  floor,  or  by  the  recoil  of  a  compressed  spring. 

(6)  Elasticity  of  Traction  (pulling) ;  it  is  illustrated  by 
a  rubber  band  stretched  around  a  book  and  holding  it  shut. 

(c)  Elasticity  of  Flexion  (bending) ;  it  is  shown  by  the 
vibration  of  a  tuning  fork,  or  of  a  steel  wire  one  end  of  which 
is  clamped  in  a  vise. 

(d)  Elasticity  of  Torsion  (twisting) ;  an  example  is  the  un- 
twisting of  a  rubber  tube  when  it  is  held  at  one  end  and  the 
other  let  go  after  being  twisted. 

17.  Hooke's  Law ;  Elastic  Limit.  —  If  different  weights 
are  suspended  from  the  hook  of  a  spring  balance,  it  will 
be  found  that  the  stretch  of  the  spring  for  a  three-pound 
weight  is  three  times  as  great  as  for  a  one-pound  weight, 
and  that  the  stretch  for  six  pounds  is  twice  as  great  as  for 
three.  Further  experiment  will  prove  that  up  to  a  certain 
point  the  elongations  of  any  spiral  spring  are  proportional 
to  the  weights  used,  and  that,  the  spring  returns  exactly  to 
its  original  length  as  soon  as  the  weight  is  removed.  But 
if  too  great  a  weight  is  put  upon  the  spring,  a  permanent 
change  in  its  shape  is  brought  about  and  the  pull  is  said  to 
have  exceeded  the  elastic  limit  of  the  spring.  The  above 
experiment  illustrates  only  one  case  of  a  law  stated  by  Robert 
Hooke  in  1676  and  now  known  as  Hooke's  Law.  This  is 


GENERAL  PROPERTIES  19 

that  ivhenever  the  forces  that  produce  distortions  in  any  body 
are  within  the  elastic  limit,  the  distortions  produced  are  directly 
proportional  to  the  forces  that  produce  them. 

The  loads  suspended  from  vertical  rods  of  the  same  material 
and  form,  when  the  elastic  limit  is  reached,  are  directly  proportional 
to  the  sizes  of  the  rods,  as  determined  by  measuring  the  areas  of  their 
cross  sections.  Hence  the  elastic  limit  of  a  substance,  for  elasticity 
of  traction,  is  usually  expressed  in  pounds  per  square  inch,  or  kilo- 
grams per  square  centimeter,  of  cross  section. 

18.  Elastic  Fatigue.  —  When  a  force  that  does  not  ex- 
ceed the  elastic  limit  is  applied  to  a  solid  for  a  long  time, 
the  change  of  form  may  slowly  continue ;  and  when  the  force 
is  removed,  the  body  may  not  return  exactly  to  its  original 
form.     This  result  is  due  to  elastic  fatigue  and  indicates  a 
permanent  change  in  the  relative  positions  of  the  molecules 
of  the  body. 

19.  Measurement  of  Elasticity.  —  If  a  load  of  4200  Ib.  is 
suspended  from  a  copper  rod  100  in.  long  and  1  sq.  in.  in 
cross  section,  the  rod  will  be  stretched  slightly  until  it  is 
100.02    inches   long.     The    external    force    (weight    of   the 
load)  tending  to  produce  elongation  will  then  be  exactly 
counterbalanced  by  the  elastic  force  produced  in  the  rod 
and  tending  to  restore  its  original  size  and  shape;  and  the 
load  will  remain  at  rest.     The  external  force  and  the  equal 
restoring  force,  in  any  case  of  elasticity,  are  each  called  a 
stress;  the  change  of  size  or  shape  in  the  body  is  called  a 
strain.    So  long  as  the  elastic  limit  is  not  exceeded,  the 
elasticity  of  any  body  is  measured  by  the  ratio  of  stress  to 
strain ;  that  is, 

Stress     Force  applied  /1 , 

Elasticity  =  ^-  .  -  =  ^  (1) 

Strain     Change  produced 


20 


THE  PROPERTIES  OF  MATTER 


In  accordance  with  this  expression  the  elastic  limit  may  be 
defined  as  the  maximum  force  that  can  be  applied  to  a  body 
without  producing  a  permanent  change  in  its  volume  or  form. 
It  is  commonly  said  that  rubber  is  very  elastic,  because  it 
can  be  stretched  to  two  or  three  times  its  length  without 
exceeding  its  elastic  limit;  that  is,  it  has  a  wide  range  of 
perfect  elasticity.  But  as  measured  in  physics,  substances 
like  copper,  steel,  marble,  and  ivory  are  far  more  highly  elastic 

than  rubber,  because 
a  much  greater  force 
is  required  to  pro- 
duce a  given  change 
in  them. 

In  the  measure- 
ment of  elasticity 
many  devices  are 
used.  One  for  test- 
ing the  torsion,  or 
twist,  of  a  rod  is 
shown  in  Fig.  3.  This 
consists  of  some  form 
of  stable  clamp  to  which  one  end  of  the  rod  is  fastened. 
The  other  end  of  the  rod  is  clamped  in  the  axis  of  a  wheel  to 
the  rim  of  which  the  twist  is  applied  by  weights.  The  read- 
ing pointer  may  be  fastened  to  the  rod  at  any  distance  from 
the  fixed  clamp  and  on  making  the  experiment  the  relation 
between  the  weights  used  (stress)  and  the  twist  (strain) 
produced  is  determined.  The  following  results  of  an  ex- 
periment will  serve  as  an  example  of  the  method. 

The  rod  was  of  cypress,  1  cm.  square  and  100  cm.  long. 
An  examination  of  the  curve  (Fig.  4)  shows  that  the  twist 
was  proportional  to  the  pull  up  to  1100  g.  Beyond  that 


FIG.  3 


GENERAL  PROPERTIES 


21 


pull  it  was  not.     That  is,  the  limit  of  elasticity  was  reached 
at  that  point. 

Demonstration.  —  Make  a  paste  by  rubbing  some  lampblack 
into  kerosene,  and  put  a  thin  coating  upon  a  flat  slab  of  iron  or  stone. 
Place  a  large  marble  upon  the  slab.  Notice  how  small  a  part  of 
the  marble  touches  the  slab.  Drop  the  marble  from  a  height  of 

PULL  TWIST 


2000 

0 
1000 
200 
300 
400 
500 
600 
700 
800 
900 
1000 
1100 
1200 
1300 
1400 
1500 
1600 
1700 
1800 
1900 

0 
4.1° 
7.6° 
11.6° 
15.2° 
18.9° 
22.5° 
26.0° 
29.8° 
33.2° 
36.9° 
40.4° 
45.0° 
50.2C 
56.1° 
61.2° 
66.5° 
72.8° 
79.1° 
87.3° 

X 

/ 

• 

X 

/ 

1400 
1200 
1000 
800 
600 
400 
200 

/ 

/ 

/ 

/ 

/ 

/ 

/ 

/ 

/ 

/ 

. 

/ 

/ 

/ 

/ 

/ 

/ 

10g      20°      30*      40s      50°      60J      70°       80°     ,909     100° 
FIG.  4 

6  or  8  ft.,  and  notice  both  the  height  to  which  'b  rebounds  and  the 
increased  size  of  the  contact  between  the  marble   and  the  slab. 
Repeat  with  a  steel  ball  such  as  would  be  used  in  ball  bearings, 
and  with  a  small  rubber  ball. 

20.  Cohesion  and  Adhesion.  —  Cohesion  is  the  mutual 
attraction  that  particles  of  the  same  kind  have  for  each 
other  at  molecular  distances.  It  is  measured  by  the  force 
required  to  pull  a  body  apart. 


.  22  THE   PROPERTIES  OF  MATTER 

If  the  attraction  is  between  particles  of  different  kinds, 
it  is  called  adhesion.  Both  of  these  attractions  are  molec- 
ular; there  is  no  essential  difference  between  them,  and 
no  need  of  two  names.  Cohesion -is  very  great  in  solids, 
and  serves  to  give  them  form  and  strength.  In  liquids 
cohesion  is  not  strong  enough  to  determine  •  the  form,  except 
in  very  small  quantities,  when  they  take  the  form  of  drops. 
In  gases  cohesion  is  very  slight.  In  many  cases  adhesion 
is  greater  than  cohesion,  as  in  the  case  of  two  boards  glued 
together,  or  two  pieces  of  china  cemented  to  each  other; 
if  they  are  again  broken,  the  break  will  be  more  likely  to  take 
place  in  the  board  or  china  than  in  the  joint.  Finely  divided 
matter  is  often  made  into  a  solid  body  by  compression,  as 

in  the  making  of  emery  wheels.    If 
a  piece  of  rubber  gum  is  cut  with  a 
knife,  the  two  pieces  may  be  made 
FlG.  5  to  cohere  perfectly  by  pressure. 

Demonstration.  —  Press  together  two  pieces  of  plate  glass  as  in 
Fig.  5,  and  see  whether  both  can  be  lifted  by  raising  the  upper  piece 
by  the  corner.  Put  two  or  three  drops  of  water  between  the  plates, 
and  they  will  cling  together  more  firmly.  Why  ? 

II.    SPEQIFIC   PROPERTIES 

21.  Tenacity.  —  When  a  body  resists  forces  that  tend 
to  pull  it  apart,  the  substance  of  which  it  is  composed  is  said 
to  be  tenacious.  Tenacity  is  a  direct  result  of  cohesion,  a 
tenacious  substance  being  one  that  has  great  cohesion.  The 
tenacity  of  a  substance  is  measured  by  the  breaking  weight  per 
unit  area  of  cross  section. 

The  tenacity,  or  tensile  strength,  of  steel  is  of  great  im- 
portance on  account  of  the  extensive  use  of  this  material  in 
building  operations.  There  are  many  grades  of  steel,  but 


SPECIFIC   PROPERTIES 


23 


most  of  them  have  a  tensile  strength  between  60,000  and 
100,000  pounds  per  square  inch. 

Demonstration.  —  To  determine  the  breaking  weight  of  No.  24 
copper  wire,  make  a  loop  in  one  end  and  suspend  it  from  a  hook 
overhead.  Fasten  a  pail  to  the  other  y* 

end  so  that  it  will  be  three  or  four  inches 
above  a  table.  Place  known  weights  in 
the  pail  until  the  wire  begins  to  stretch, 
then  slowly  pour  in  sand  until  the  wire 
breaks. 

By  measuring  the  diameter  of  the  wire 
and  taking  the  weight  of  the  total  load, 
the  tensile  strength  can  be  computed,  by 
dividing  the  breaking  weight  by  the  area 
of  cross  section.1  (For  example,  if  a  wire 
TV  in.  in  diameter  is  broken  by  a  load  "of 
104  lb.,  the  tensile  strength  is  equal  to 


104 -T- 


3.1416 
32X32 


:  33,898  lb.  per  square  inch.) 


FIG.  6 


In  bodies  of  the  same  material, 
tenacity  varies  with  the  form  of  the 
body.  When  the  areas  of  cross  sec- 
tion are  equal,  a  tube  has  greater 
tenacity  than  a  solid  cylinder  of  the  same  material,  and  a 
wire  with  circular  cross  section  has  greater  tenacity  than  one 
with  a  square  cross  section. 

Tenacity  diminishes  with  the  length  of  time  the  load  is 
carried,  so  that  a  wire  may  finally  break  with  a  load  that 
it  would  carry  safely  at  first.  Tenacity  also  diminishes 
as  the  temperature  increases,  on  account  of  the  increased 
rate  of  molecular  vibration. 


1  The  area  of  a  circular  cross  section  is  equal  to  3.1416  times  the 
square  of  half  the  diameter. 


24  THE  PROPERTIES  OF  MATTER 

22.  Malleability.  —  A  substance  that  may  be  beaten  or 
rolled  into  thin  sheets  is  said  to  be  malleable.     Brass  can 
be  rolled  into  sheets  thinner  than  the  paper  of  this  book. 
Gold  leaf  is  so  thin  that  it  is  transparent. 

23.  Ductility.  —  A  substance  that  can  be  drawn  into  wire 
is  said  to  be  ductile.     Some  metals  possess  great  ductility. 
Platinum  has  been  drawn  into  wire  only  0.00003  of  an  inch 
thick.     In  order  to  do  this,  a  small  platinum  wire  was  covered 
with  silver,  forming  a  compound  cylinder,  the  silver  sur- 
rounding the  platinum  much  as  the  wood  surrounds  the 
graphite  in  a  lead  pencil.     This  cylinder  was  drawn  into  a 
very  small  wire,  which  had  still  a  platinum  center  surrounded 
by  silver;  then  the  silver  was  dissolved  by  an  acid  which 
does  not  affect  platinum,  and  the  platinum  was  left  as  a  wire 
of  microscopic  fineness. 

Demonstration.  —  Take  a  piece  of  glass  tubing  about  10  cm.  long 
by  the  ends  and  hold  the  middle  in  the  flame  of  a  Bunsen  burner 
near  the  top.  When  it  becomes  cherry  red  remove  it  from  the 
flame  and  draw  it  out  with  a  steady  pull.  Prove  that  it  is  a  tube 
by  blowing  through  it  when  one  end  is  under  the  surface  of  water. 

24.  Hardness  is  a  relative  property;  there  is  no  such 
thing  as  an  absolutely  hard  or  soft  body.     A  body  that 
can  scratch  or  wear  another  is  the  harder  of  the  two.    ^Glass 
is  harder  than  wax  but  softer  than  the  diamond.     The  dia- 
mond is  the  hardest  of  all  natural  substances,  and  diamond 
dust  is  used  to  cut  other  stones.     Brittleness  must  not  be 
mistaken   for  hardness.     Steel,   which  is  hard,   is  tough; 
while  glass,  which  is  also  hard,  is  brittle. 

Steel  is  rendered  very  hard  and  brittle  by  being  heated  to  a 
red  heat  and  then  being  plunged  into  water.  In  order  to 
render  it  serviceable  for  cutting  tools,  or  for  springs,  it  is 


SPECIFIC  PROPERTIES  25 

reheated  slowly  until  it  has  the  desired  degree  of  hardness, 
which  is  indicated  by  its  color,  when  it  is  again  plunged  into 
water  or  oil.  This  process  is  called  tempering. 

Iron  may  be  rendered  soft,  or  annealed,  by  cooling  it  grad- 
ually and  evenly  from  a  high  temperature.  This  renders 
iron  wire  pliable,  and  if  the  same  process  is  applied  to  glass, 
the,  strains  are  taken  out  and  it  is  much  less  liable  to  crack 
on  being  heated. 

A  swiftly  moving  body  will  cut  one  that  is  at  rest  even 
if  the  latter  is  harder,  as  in  the  case  of  a  soft  iron  disk  ro- 
tating at  a  high  speed,  which  is  sometimes  used  to  cut  off 
hard  steel  bars.  The  cutting  power  of  an  emery  or  car- 
borundum wheel  depends  both  upon  the  hardness  of  the 
material  and  the  high  speed  at  which  it  is  run.  A  buffing 
wheel  used  for  polishing  metals  is  an  example  of  this  action. 

25.  Crystallization.  —  Some  matter  in  the  form  of  a  solu- 
tion has  the  property  of  forming  crystals.  Crystals  may 
also  be  formed  when  a  melted  metal  solidifies  on  cooling. 
Zinc  shows  this  very  plainly  on  account  of  tHe  size  of  its 
crystals.  If  a  bar  of  cast  zinc  is  broken,  not  only  can  the 
crystals  be  seen,  but  a  line  of  weakness  will  be  shown  wherever 
they  meet  from  the  sides  of  the  mold. 

By  a  saturated  solution  is  meant  one  that  will  take  up  no  more 
of  the 'substance.  When  salt  is  put  into  water  until,  after  thorough 
stirring,  some  of  tHe  salt  is  still  not  dissolved,  the  solution  is  said  to  be 
saturated.  When  such  a  solution  begins  to  evaporate,  crystals 
are  formed.  Raising  the  temperature  of  a  solution  usually  causes 
more  of  the  substance  to  be  dissolved  and  crystals  form  when  it 
cools. 

Demonstrations.  —  Make  a  saturated  solution  of  salt  and  put 
it  in  a  beaker.  Set  this  in  a  quiet  place,  and  after  a  few  hours 
you  will  find  the  surface  of  the  liquid  covered  with  little  cubical 


26 


THE   PROPERTIES  OF  MATTER 


FIG.  7.  —  Ice  Crystals.     Frost  on  a  Window 


SPECIFIC  PROPERTIES 


27 


crystals  of  salt.     Let  the  solution  stand  for  twenty-four  hours  and 

groups  of  crystals  will  be  floating  on  the  surface.     Lift  one  of  these 

out,  invert  it,  and  you 

will  find  a  beautiful  little 

pyramid  formed  of  salt 

cubes. 

Make  a  saturated 
solution  of  salt  and  fill 
a  teacup  nearly  full. 
Set  the  cup  in  a  saucer 
and  put  them  in  some 
quiet  place.  In  a  few 
days  the  salt  crystals 
will  creep  over  the  edge 
of  the  cup  and  form  a 
coating  upon  the  outside  FIG.  8.  —  Creeping  of  Crystals 

and  in  the  saucer. 

Make  a  solution  of  potassium  bichromate.  Pour  a  little  on  a 
clear  glass  plate,  and  with  a  small  stick  work  the  liquid  into  the  form 
of  a  flat,  round  mass.  Set  it  in  a  quiet  place  over  night,  and  then 
observe  the  crystals  with  a  reading  glass.  Beautiful  slides  can  be 
made  in  this  way  for  projection  on  the  screen  with  a  lantern. 

III.    MASS,  WEIGHT,  AND  MEASUREMENTS 

26.  Mass  and  Weight. — The    mass    of .  a    body    is    the 
amount  of  matter  in  it,  as  determined  by  " weighing"  the 
body  in  a  lever  balance.    The  weight  of  a  body,  though  de- 
pending upon  its  mass,  is  a  different  thing,  and  the  two 
words  should  not  be  confused.     The  weight  of  a  body  is 
the  measure  of  the  mutual  attraction  between  the  body  and  the 
earth.    This  attraction  varies  slightly  in  degree  at  different 
parts  of  the  earth,  while  the  amount  of  matter,  or  mass,  in 
a  pound  of  lead,  for  instance,  is  the  same  everywhere. 

27.  Measurements. —  The  modern  study  of  physics,  with 
the  accurate  knowledge  obtained  therefrom,  depends  largely 


28  ME    PROPERTIES  OF  MATTER 

upon  precise  measurements,  made  in  the  units  of  space,  mass, 
and  time.  We  shall  consider  two  systems  of  measurements, 
the  English  because  it  is  in  general  use,  and  the  French  or 
metric  because  of  its  simplicity  and  of  its  growing  use  in  all 
scientific  work. 

28.  The  C.  G.  S.  System  of  Measurement.  —  Scientists 
working  in  various  countries  felt  the  inconvenience  of  having 
various  standards  of  length,  mass,  and  time,  and  finally 
adopted,  for  scientific  work,  the  French  system,  more  pre- 
cisely known  as  the  centimeter-gram-second  or  C.   G.  S. 
system.     The  convenience  of  this  system  is  so  great  that 
it  is  taking  the  place  of  the  foot-pound-second  or  F.  P.  S. 
system,  used  in  Great  Britain  and  the  United  States. 

29.  Space    of    One    Dimension :    Length.  —  The  French 
measures  of  length  were  devised  in  the  latter  part  of  the 
eighteenth   century,   by  physicists  who   aimed  to   accom- 
plish two  things  :  first,  to  obtain  a  unit  based  upon  a  natural 
measure ;  and  second,  to  take  advantage  of  the  convenience 
of  the  decimal  scale.     To  secure  the  first  result,  they  took 
for  the  meter,  or  unit  of  length,  the  ten-millionth  part  of  the 
distance  from  the  equator  to  the  pole,  measured  on  the 
meridian   passing   through    Paris.     Subsequent   and    more 
accurate  measurements  have  shown  that  the  distance  as 
originally  measured  was  not  absolutely  correct,  and  that  the 
length  of  the  standard  meter  is  contained  in  the  quadrant 
of  the  earth  10,000,880  times.     While  this  prevents  the  meter 
from  being  the  decimal  part  of  a  natural  unit,  it  does  not 
affect  the  value  of  the  meter  as  a  practical  unit. 

The  original  standard  meter  is  a  rod  of  platinum  kept 
in  the  archives  at  Paris,  and  the  distance  between  its  ends 
at  the  temperature  of  melting  ice  is  1  meter.  The  tempera- 


MEASUREMENTS  29 

ture  has  to  be  stated  because  a  metal  bar  changes  in  length 
with  a  change  in  temperature. 

For  the  multiples  of  the  meter  the  Greek  prefixes  deka, 
hekto,  and  kilo  are  used,  and  for  the  decimal  parts  the  Latin 
prefixes  deci,  centi,  and  milli;  as  follows : 

10  millimeters   =  1  centimeter          10  meters  =  1  dekameter 

10  centimeters  =  1  decimeter  10  dekameters    =  1  hektometer 

10  decimeters     =  1  meter  10  hektometers  =  1  kilometer 

For  small  divisions  of  the  millimeter  the  micron,  one  one- 
thousandth  of  a  millimeter,  and  the  millimicron,  one  one-millionth 
of  a  millimeter,  are  used.  These  are  designated  by  the  Greek 
letters  /«,  (mu)  and  mi.  respectively.  Millimeter,  centimeter,  meter, 
and  kilometer  are  abbreviated,  respectively,  mm.,  cm.,  m.,  and  km. 

The  English  unit  of  length  is  the  yard,  which  is  defined 
by  English  law  as  "  the  distance  between  the  centers  of  the 
transverse  lines  in  the  two  gold  plugs  in  the  bronze  bar  de- 
posited in  the  office  of  the  exchequer  "  in  London,  when  the 
temperature  is  62°  Fahrenheit.  For  practical  use  the  foot  — 
one  third  of  a  yard  —  is  taken  as  the  unit. 

Copies  of  the  standard  yard  have  been  made  and  dis- 
tributed to  those  countries  that  use  the  English  systems. 
The  standard  now  used  in  the  United  States,  however,  is 


FIG.  9.  — Prototype  Meter 


derived  from  the  International  Prototype  Meter.  That  is, 
the  yard  in  this  country  is  made  f  f  fy  as  long  as  the  meter ; 
but  there  is  only  a  microscopic  difference  between  this  and 
the  English  standard. 

Seventeen  nations,  of  which  the  United  States  was  one,  united 
in  establishing  the  International  Bureau  of  Weights  and  Measures, 


30 


THE   PROPERTIES  OF  MATTER 


and  in  1889  the  international  prototype  standards,  which  were 
copies  of  the  standard  meter  and  kilogram,  were  completed  by  the 
Bureau  and  distributed  by  lot  to  the  various  nations  concerned. 
The  United  States  received  meters  Nos.  21  and  27  and 
kilograms  Nos.  4  and  20.  The  seals  of  meter  No.  27 
(Fig.  9)  and  of  kilogram  No.  20  were  broken  by  Presi- 
dent Harrison  on  Jan.  3,  1890,  and  these  standards  are 
now  in  the  custody  of  the  National  Bureau  of  Standards 
in  Washington.1 

The  relation  between  the  various  measures  of 
length  in  this  country  is  shown  below : 

1  mm.  =  0.03937  inch 

1  cm.    =  0.3937  inch 

1m.     =  39.37  inches  or  3.28083  feet 

1  km.    =  3280  feet  or  0.62137  mile 

1  in.      =  2.54  cm. 
1  ft.      =  0.3048  m. 
Imile  =  1.60935km. 

The  student  will  find  it  useful  to  become  famil- 
iar with  a  few  approximate  values  besides  the 
exact  value  of  the  meter  in  inches.  The  millimeter 
is  nearly  equal  to  ^V  of  an  inch,  the  centimeter  to 
f  of  an  inch,  the  kilometer  to  f  of  a  mile. 

To  use  any  scale  intelligently  one  must  have  a 
distinct  idea  of  the  values  of  the  units.  To  secure 
this  in  the  metric  scale  the  student  should  measure 
many  familiar  objects  with  the  metric  scale  in 
terms  of  the  centimeter,  as  that  is  commonly  taken 
as  the  unit  of  length  in  physics. 

30.  Space  of  Two  Dimensions :  Surfaces.  —  Since  a  sur- 
face has  but  two  dimensions,  the  unit  of  surface  is  a  square 


FIG.  10.— 
1  Deci- 
meter 


1  See  Bulletin  No.  26,  U.  S.  Coast  and  Geodetic  Survey,  "Funda- 
mental Standards  of  Length  and  Mass." 


MEASUREMENTS  31 

of  which  the  unit  of  length  is  the  side.  In  most  physical 
measurements  the  unit  of  surface  is  the  square  centimeter 
(sq.  cm.  or  cm.2),  though  for  small  areas  the  square  millimeter 
(sq.  mm.  or  mm.2)  is  commonly  used.  The  table  is  similar 
to  the  table  for  length,  but  with  a  uniform  scale  of  100 ;  that 
is,  100  sq.  mm.  =  1  sq.  cm.,  or  100  mm.2  =  1  cm.2,  etc. 

31.  Space  of  Three  Dimensions  :  Solids.  —  A  volume  has 
three  dimensions,  length,  breadth,  and  thickness.     The  unit 
of  volume  is  a  cube  with  the  unit  of  length  for  each  edge.     In 
the  metric  system  it  is  the  cubic  centimeter  (c.c.  or  cm.3),  and 
the  scale  of  the  table  is  1000. 

Units  of  Mass  and  Weight.  —  The  French  standard  mass 
is  the  kilogram  (kg.).  This  is  the  mass  of  a  cubic  decimeter 
of  pure  water  at  4°  C.  The  gram  (g.) ,  equal  to  one  thousandth 
of  the  kilogram,  is  the  practical  unit'  in  physics.  Decimal 
subdivisions  and  multiples  of  the  gram  are  named  by  using 
the  same  prefixes  as  with  the  meter.  The  standard  pound 
in  this  country  is  derived  from  the  International  Prototype 
Kilogram.  The  exact  relation  is,  1  Ib.  =  0.4535924277  kg. ; 
but  for  ordinary  purposes  the  following  are  used  as  equiva- 
lents :  1  kg.  -  2.2046  Ib.  1  Ib.  =  0.4536  kg. 

Since  at  any  one  place  the  weights  of  bodies  are  directly  propor- 
tional to  their  masses,  and  since  the  variation  in  weight  with  location 
on  the  earth's  surface  is  not  very  great,  the  terms  that  are  applied 
to  masses  (gram,  pound,  ounce,  etc.)  are  commonly  applied  to  the 
corresponding  weights  also. 

It  is  often  important  in  physics  to  compare  the  masses  of  equal 
volumes  of  different  substances,  or  the  volumes  of  equal  masses. 
By  the  density  of  a  body  is  meant  the  ratio  of  its  mass  to  its  volume, 
or  the  mass  of  a  unit  volume. 

32.  Capacity.  —  Measures  of  capacity  in  the  metric  sys- 
tem depend  upon  the  unit  of  length,  the  unit  of  capacity 


32  THE  PROPERTIES  OP  MATTER 

being  a  cubic  decimeter,  which  is  called  the  liter.  As  this 
is  1000  c.c.,  a  liter  of  pure  water  at  the  temperature  of  great- 
est density  weighs  1  kg. 

33.  Time. — The  unit  of  time  in  physics  is  the  second. 
This  is  the  second  of  mean  solar  time,  and  is  je^Fo  °f  the 
mean  solar  day.  Mean  solar  time  is  the  time  in  common 
use,  recorded  by  clocks  and  watches. 

According  to  Albert  Einstein's  theory  of  relativity,  time  and 
mass  and  dimensions  vary  with  the  velocity  of  the  motion  of  the 
body  concerned.  This  variation  is  important  for  very  great  veloci- 
ties, comparable  with  the  velocity  of  light,  but  for  moderate  veloci- 
ties it  is  so  infinitesimally  small  as  to  have  no  effect.  Hence  time 
and  the  masses  and  measurements  of  ordinary  bodies  in  physics  are 
not  affected  by  this  theory. 

Questions 

1.  A  piece  of  paraffin  wax  is  heated  until  it  melts.     The  melted 
paraffin  is  then  heated  until  it  burns.     Name  the  changes  that  have 
taken  place. 

2.  What  kind  of  change  takes  place  when  salt  is  put  in  water? 
How  may  the  salt  be  regained  ? 

3.  What   different  forms   can  water  be  made  to  assume  by 
changing  its  temperature?    Describe  each. 

4.  Suppose  you  wish  to  pour  a  liquid  into  a  bottle,  using  a  funnel. 
Should  you  use  a  funnel  that  fits  the  mouth  of  the  bottle  air-tight  ? 
What  is  the  reason  for  your  answer? 

5.  Show  how  you  would  find  the  volume  of  a  piece  of  coal  by 
displacement. 

6.  Suppose  you  make  a  solution  of  salt  and  mix  some  chalk 
dust  in  it.    What  will  be  the  result  of  filtering  the  solution  ?   Explain. 

7.  What  is  changed  when  a  gas  is  compressed,  the  size  of  the 
molecules  or  the  distance  between  them? 

8.  How  does   the   surface   of  writing  paper  differ  from  that 
of  blotting  paper? 

9.  Give  examples  of  cohesion  and  adhesion. 


MEASUREMENTS  33 

10.  Upon  what  property  of  matter  does  the  strength  of  a  kite 
string  depend? 

11.  How  could  you  find  which  is  harder,  glass  or  diamond? 

12.  Are  the  divisions  of  the  scale  of  a  spring  balance  of  equaJ 
length?     Why? 

Problems 

1.,  A  runner  makes  a  100-yard  dash  in  9.5  seconds.     What  is  his 
speed  in  feet  per  second?    In  meters  per  second? 

2.  The  Eiffel  Tower  is  335  m.  high.     How  many  feet  high  is  it? 

3.  The  Washington  Monument  is  555  ft.  high.     Give  its  height 
in  meters. 

4.  It  is  535  feet  from  the  top  of  the  statue  of  William  Penn  on 
the  City  Hall  tower  in  Philadelphia  to  the  pavement  at  the  foot  of 
the  tower.     How  far  is  it  in  meters? 

6.  A  boy  5  ft.  2  in.  tall  weighs  104  Ib.     Find  his  height  in  centi- 
meters and  his  weight  in  kilograms. 

6.  The  distance  from  the  Pennsylvania  station,  New  York,  to 
the  Broad  Street  station  in  Philadelphia  is  91.3  miles.     How  many 
kilometers  is  it? 

7.  The  airline  distance  from  Paris  to  London  is  338  kilometers. 
What  is  the  distance  in  miles? 

8.  A  pile  of  wood  8  ft.  long,  4  ft.  wide,  and  4  ft.  high  contains 
one  cord.     How  many  cubic  meters  does  it  contain? 

9.  A  block  of  marble  4  ft.  long,  3  ft.  wide,  and  1^  ft.  high  weighs 
2970  Ib.    What  is  its  weight  in  pounds  per  cubic  foot?    What  is  its 
weight  in  kilograms  per  cubic  foot? 

10.  How  many  kilograms  in  a  ton  of  2000  Ib.? 

11.  How  many  long  tons  (2240  Ib.)  in  10  metric  tons?     (1  metric 
ton  =  1000  kg.) 

12.  A  cubical  box  is  2  meters -on  each  edge,  inside.     How  many 
liters  of  water  will  be  required  to  fill  it?    What  will  the  water  weigh 
in  kilograms?    In  pounds? 

13.  A  barrel  of  flour  weighs  196  Ib.    What  is  its  weight  in  kilo- 
grams? 

14.  A  metal  bar  2  inches  square  is  pulled  apart  by  a  load  of  56,326 
Ib.    Compute  the  tensile  strength  of  the  metal,  per  square  inch  of 
cross  section. 

Rev. 


CHAPTER  III 
THE  MECHANICS   OF   SOLIDS 

I.   MOTION,   VELOCITY,   AND  FORCE 

34.  Mechanics  treats  of  the  action  of  forces  on  bodies. 
It  may  be  divided  into  two  subjects,  statics  and  dynamics. 
Statics  treats  of  the  laws  governing  forces  when  no  motion 
is  produced,  and  Dynamics  or  Kinetics  treats  of  the  laws 
governing  forces  by  which  motion  is  produced. 

35.  Motion.  — A  body  is  said  to  have  motion  while  it  is 
passing  continuously  from'  one  position  to  another.     A  body 
is  at  rest  when  its  position  remains  unchanged. 

An  automobile  standing  by  the  curb  is  at  rest.  When 
the  engine  is  started  and  its  power  applied,  the  automobile 
begins  to  move.  That  is,  by  the  application  of  sufficient 
force  its  condition  is  changed  from  rest  to  motion.  Rest  and 
motion  are,  however,  entirely  relative.  A  body  may  be  at 
rest  in  a  railroad  train,  but  in  motion  with  respect  to  the 
earth.  A  body  that  is  at  rest  with  respect  to  the  earth  is  in 
motion  with  respect  to  the  sun. 

The  motion  of  a  body  is  said  to  be  rectilinear  when  it 
moves  in  a  straight  line.  When  a  body  moves  in  a  path 
which  constantly  changes  in  direction,  it  is  said  to  have  a 
curvilinear  motion,  or  to  move  in  a  curve.  While  it  may 
not  be  difficult  to  imagine  a  body  moving  from  one  fixed 
point  in  space  toward  another  without  change  of  direction, 
in  strict  reality  we  know  of  no  absolutely  rectilinear  motion 

34 


MOTION,  VELOCITY,  AND  FORCE 


35 


36  THE  MECHANICS  OP   SOLIDS 

of  bodies.  A  stone  falling  from  a  balloon  is  moving  toward 
the  center  of  the  earth,  but  this  is  itself  moving  about  the 
sun,  hence  the  motion  of  the  stone  must  be  in  a  curve.  For 
all  practical  purposes,  however,  a  body  which  moves  without 
change  of  direction  with  reference  to  a  room  or  the  surface 
of  the  earth  is  said  to  move  in  a  straight  line. 

If  a  body  moves  over  equal  spaces  in  equal  times,  its  motion 
is  said  to  be  uniform.  If  the  distances  are  not  equal,  its 
motion  is  variable. 

36.  Speed ;  Velocity.  —  Speed   is   the   rate   of  change  of 
position  of  a  moving  body  or  its  rate  of  motion;    velocity 
is  the  speed  in  a  definite  direction.     If  the  motion  is  uni- 
form, the  speed  is  measured  by  the  distance  the  body  goes 
in  a  unit  of  time.     If  the  motion  is  variable,  the  speed  at 
any  instant  is  the  distance  it  would  move  during  the  next 
unit  of  time  if  it  should  continue  to  move  at  the  same  rate. 

If  the  speed  of  a  body  is  greater  for  each  unit  of  time 
than  it  was  for  the  preceding,  the  motion  is  said  to  be  ac- 
celerated. If  the  acceleration,  or  increase  of  speed,  is  the  same 
for  each  unit  of  time,  the  motion  is  uniformly  accelerated. 

Motion  is  retarded,  or  negatively  accelerated,  when  the 
speed  is  decreasing  instead  of  increasing,  and  if  the  retarda- 
tion is  uniform,  the  motion  is  uniformly  retarded. 

Average  or  mean  speed  is  the  speed  with  which  a  body 
would  need  to  move  uniformly  to  pass  over  a  certain  space 
in  a  given  time,  though  the  actual  speeds  may  be  made  up 
of  a  great  many  rates. 

If  only  motion  in  a  definite  direction  is  considered,  the  above 
statements  about  speed  will  also  hold  true  of  velocity. 

37.  Space  Passed  Over.  —  The  space  passed  over  by  a 
moving  body  depends  upon  two  elements,  speed  and  time. 


MOTION,  VELOCITY,  AND  FORCE  37 

A  train  moving  with  an  average  speed  of  20  mi.  per  hour 
moves  60  mi.  in  3  hr.  This  relation  may  be  expressed  by 
the  equation  60  =  20  X  3 ; 

so  in  general, 

Space  passed  over  =  Average  speed  X  Time, 

or,  writing  S  for  space  passed  over,  v  for  average  speed,  and 
t  for  time,  we  have  the  formula 

S  =  vt.  (2) 

NOTE.  —  The  student  should  observe  that  "  Space  passed 
over  =  Average  speed  X  Time  "  is  not  to  be  understood  literally. 
It  is  merely  a  short  and  convenient  way  of  saying,  "  The  number  of 
units  of  length  passed  over  =  the  number  of  units  of  length  in  the 
average  speed  per  unit  of  time  X  the  number  of  units  of  time." 
The  briefer  wording  of  such,  formulas  as  this  is  so  convenient  and 
so  commonly  employed  in  actual  use,  that  it  will  be  used  in  this 
book;  but  the  student  should  always  bear  in  mind  that  every 
element,  or  letter,  in  a  formula  represents  merely  a  number. 

38.  Acceleration.  —  When  the  velocity  of  a  body  is  uni- 
formly accelerated,  the  rate  of  change  in  its  velocity  or  the 
amount  its  velocity  changes  per  second,  is  called  its  accelera- 
tion. If  the  body,  starting  from  a  condition  of  rest,  has  a 
velocity  of  2  ft.  per  second  at  the  end  of  one  second,  4  ft.  per 
second  at  the  end  of  the  next  second,  6  at  the  end  of  the  third, 
and  so  on,  the  gain  in  velocity,  per  second,  is  2  ft.  per  second ; 
that  is,  the  acceleration  is  2  ft.  per  second  per  second.  In 
uniformly  accelerated  motion  the  average  velocity  for  any 
period  is  half  of  the  sum  of  the  velocities  at  the  beginning 
and  end  of  that  period.  Hence  in  this  case,  as  the  velocity  is 
0  at  the  beginning,  the  average  velocity  for  the  first  second 
would  be  1  ft.  per  second,  and  the  average  velocity  for  the 
first  three  seconds  would  be.  3  ft.  per  second. 


38  •    THE  MECHANICS  OF  SOLIDS 

Suppose  a  body  to  move  in  a  certain  direction  from  a 
condition  of  rest  with  a  constant  acceleration  of  a  units  per 
second  per  second.  Its  velocity  per  second  at  the  end  of  1 
sec.  will  be  a ;  at  the  end  of  2  sec.,  2  a ;  at  the  end  of  3  sec., 
3  a ;  and  so  on.  At  the  end  of  t  seconds  its  velocity  per 
second  will  be  t  X  a  or  at ;  that  is, 

Final  velocity  =  Acceleration  X  Time, 
or,  v  —  at.  (3) 

Since  the  velocity  per  second  increases  uniformly  from 
0  at  the  beginning  to  at  at  the  end  of  t  seconds,  the  average 
velocity  per  second  for  t  seconds  will  be  f  at,  and  the  entire 
space  passed  over  equals  average  velocity  X  time.  This  may 
be  represented  by  the  equation 

S  =  i  at  X  t  =  %  at2.  *  (4) 

Since  the  velocity  per  second  for  the  first  second  increases 
uniformly  from  0  at  the  beginning  to  a  at  the  end,  the  space 
passed  over  in  that  second  will  be  f  a.  We  can  get  the  same 
result  by  making  the  time  1  sec.  in  Equation  4,  for  the  equa- 
tion then  becomes  S  =  |  a.  We  see  from  this  that  whenever 
a  body  starts  from  a  condition  of  rest,  and  moves  with  a 
constant  acceleration,  the  acceleration  per  second  per  second 
is  twice  the  space  passed  over  in  the  first  second. 

The  space  passed  over  during  any  second  (the  last  of  t 
seconds)  may  be  found  by  subtracting  from  the  distance 
passed  over  in  t  seconds  the  distance  passed  over  in  a  time 
one  second  less.  The  space  passed  over  in  t  seconds  be- 


1  By  combining  Equations  3  and  4  we  can  derive  the  equation 

S  =  —  ;  and  from  this,  v  =  V2^,  (5) 

2a 

a  formula  sometimes  convenient  for  finding  the  final  velocity  directly 
frem  the  acceleration  and  the  entire  space  passed  over. 


MOTION,   VELOCITY,  AND  FORCE  39 

ing  by  Formula  4,  S  =  f  at2,  the  space  passed  over  in  (t  —  1 ) 
seconds  will  be  Sf  =  f  a(t  —  I)2.  Hence  the  space  passed 
over  in  the  last  second  will  be 

S  =  S-S'  =  \a$-\a(t-  I)2  =  io(2<- 1);  i.e., 

s  =  ±a(2t-l).  (6). 

It  is  sometimes  convenient  to  express  velocity  and  acceleration 
in  symbols.  Thus  a  velocity  of  twenty  centimeters  per  second  may 

be  expressed  as  20  ^^,  and  the  speed  of  a  bicycle  rider  going  at  the 
sec.  ^ 

rate  of  a  mile  in  four  minutes  is  a  speed  of  22  —^—,  that  is,  twenty-two 

sec.' 

feet  per  second.     In  the  same  way  an  acceleration  of  fifteen  centime- 

(*»YY"i 

ters  per  second  per  second  may  be  written  15  — '-,  and  an  aecelera- 

sec.  £^ 

tion  of  twelve  feet  per  second  per  second  may  be  written  12  — '—^. 

39.  Effect  of  a  Constant  Force.  —  Whenever  a  body  is 
moving  under  the  influence  of  a  constant  force  only  and  there 
is  no  change  in  the  resistance,  the  resulting  motion  is  uni- 
formly accelerated.     The  constant  force  with  which  we  are 
most  familiar  is  the  force  of  gravity ;  hence,  as  an  illustration 
of  the  effect  of  constant  forces,  we  study  the  motion  of  a 
falling  body. 

40.  A  Freely  Falling  Body ;  Resistance  of  the  Air.  —  A 

body  that  is  moving  under  the  influence  of  gravity  alone 
is  a  freely  falling  body.  This  condition  can  be  obtained  only 
in  a  vacuum,  as  the  air  constantly  offers  a  resistance  to  the 
passage  of  any  body  through  it. 

Demonstrations.  —  Trim  a  piece  of  stiff  paper  and  a  cork  until 
each  has  the  same  weight  as  a  shot  or  a  bicycle  ball.  Drop  all  three 
from  the  same  height  at  exactly  the  same  time,  and  notice  when 
they  strike  the  floor.  Since  they  all  have  the  same  weight,  the  force 
tending  to  give  them  motion  is  the  same,  but  as  they  present  dif- 


40  THE  MECHANICS  OF  SOLIDS 

ferent  amounts  of  surface  to  the  air,  the  resistance  of  the  air  varies, 
If  the  sheet  of  paper  is  let  fall  when  it  is  flat,  it  will  slide  down  on  the 
air  in  various  directions,  but  if  a  small  part  of  its  width  is  turned 
up  at  an  angle,  it  will  fall  very  steadily. 

Drop  two  balls  of  the  same  size,  one  of  brass  and  one  of  wood, 
from  a  height  of  20  ft.  or  more.  They  reach  the  ground  at  practi- 
cally the  same  time.  Why? 

These  demonstrations  indicate  in  a  simple  way  the  method 
used  by  Galileo  to  settle  by  experiment  the  discussion  which 
had  been  vigorously  carried  on  between  those  who  thought 
that  the  velocity  of  a  freely  falling  body  was  proportional 
to  its  weight  and  those  who,  like  Galileo,  thought  it  was 
the  same  for  all  bodies.  The  experiment  was  made  by  drop- 
ping various  bodies  from  the  top  of  the  leaning  tower  of  Pisa, 
and  showed  that  Galileo  was  right.  The  pull  of  the  earth  on 
a  two-pound  weight  is  twice  its  pull  on  a  one-pound  weight, 
but  in  causing  the  weights  to  fall  this  pull  must  do  twice  as 
much  work  on  the  two-pound  weight  as  on  the  one-pound 
weight ;  hence  the  speed  of  the  fall  is  the  same.  The  re- 
sistance of  the  air  prevents  raindrops  from  acquiring  a  high 
velocity.  A  parachute  (Fig.  12)  likewise  falls  slowly  because 
it  presents  a  surface  that  is  large  in  proportion  to  the  weight. 

41.  Measuring  the  Velocity  of  Falling  Bodies.  —  (a)  The 
Direct  Method  consists  of  dropping  a  small  ball  of  some  heavy 
material  from  the  top  of  a  tower  —  like  a  shot  tower  —  and 
determining  by  actual  measurement  where  it  strikes  a  sup- 
port at  the  end  of  the  first  second,  second  second,  etc.  One 
of  the  difficulties  connected  with  this  method  is  the  height  of 
tower  required,  since  for  a  fall  of  3  sec.  the  tower  would 
need  to  be  about  145  ft.  high. 

(6)  Galileo's  Method.  In  all  other  methods  the  velocity 
of  the  falling  body  is  reduced  in  some  way.  Galileo  ac- 


MOTION,   VELOCITY,   AND   FORGE  41 


FIG.   12.  —  A  Parachute  in  Action,  as  seen  from  an  Airplane 

The  parachute  was  first  used  for  making  a  spectacular  descent  from  a  balloon.  Dur- 
ing and  after  the  World  War  of  1914-1918,  parachutes  were  put  to  practical  use  in  mak- 
ing descents  from  balloons,  dirigibles,  and  airplanes. 


42, —r 


.TilK   MECHANICS  OF  SOLIDS 


FIG.  13 


TABLE  A 


a 

£•§ 
ii 


i 


complished  this   by  letting  a  ball   roll  down  an  inclined 
plane.     If  the  length  of  the  plane  is  made  great  in  com- 

A  parison  with  the  height, 
1  I  the  ball  will  roll  down  the 
plane  far  more  slowly 
than  it  would  fall  in  a 
vertical  direction. 
If  the  experiment  is  carefully  made,  the  results  will  be 
such  as ,  are  shown  in  Table  A,  since  the  resistance  of  the 
air  is  slight.  Let  A  1  (Fig.  13),  the  space  passed  over  in  the 
first  second,  be  called  d.  Then 
it  will  be  found  that  A  2,  the 
space  passed  over  in  2  seconds, 
is  4  times  as  great,  or  4  d ;  that 
A3,  the  space  passed  over  in  3 
seconds,  is  9  times  as  great,  or 
9  d,  etc.,  no  matter  what  the 
proportional  height  of  the  plane 
is.  These  results  are  shown  in 
the  fourth  column  of  Table  A, 
from  which  are  found  the  spaces 
passed  over  in  the  different  sec- 
onds, as  shown  in  the  third  col- 
umn. Since  the  force  is  a  constant  one  (it  is  a  certain 
fraction  of  the  weight  of  the  ball),  the  acceleration  is  con- 
stant, and  is  twice  the  distance  passed  over  in  the  first  sec- 
ond, or  2  d,  per  second  per  second.  Notice  that  this  is 
also  the  difference  between  any  two  successive  values  in 
column  3.  The  acceleration  2  d  in  turn  gives  the  values 
in  the  second  column. 

By  increasing  the  proportional  height  of  the  plane  the 
velocity  of  the  ball  is  increased,  until,  when  the  plane  becomes 


2d 

4d 

Sd 


d 
3d 

Id 


9d 
16  d 


MOTION,  VELOCITY,  AND   FORCE 


43 


vertical,  the  ball  is  no  longer  a  rolling  but  a  falling  body  and 
the  acceleration  equals  g,  the  acceleration  due  to  gravity. 

Replacing  a  in  Formulas  3,  6,  and  4  by  g,  we  have  the 
formulas  for  falling  bodies  : 

v  =  gt,  (7) 

jr.-  iflr(2*-l),  (8) 

S  =  ±gt*.  (9) 

The  value  of  g  varies  at  different  places  on  the  earth,  from 
about  978  cm.  at  the  equator  to  about  983  cm.  at  the  poles. 
At  New  York  its  value  is  980.2  cm.,  or  32.16  feet.  By  making 
this  substitution,  these  formulas  may  be  written : 


FOR  RESULTS  IN  FEET 


FOR  RESULTS  IN  CENTIMETERS 


v  =•  32.16  t  or  v  =  980.2  t, 

s  =  16.08(2  t  -  1)  or  *  =  490.1(2  *  -  1), 

8  =  16.08  *2  or  S=  490.1  Z2. 

JL 


These  formulas  for  freely  fall- 
ing bodies  are  very  important, 
and  should  be  familiar  to  every 
student. 

42.  Graphical  Analysis  of  a 
Falling  Body.  —  The  motion 
of  a  falling  body  can  be  an- 
alyzed graphically  as  in  Fig. 
14.  Draw  a  vertical  line  and 
take  a  certain  distance  AB, 
from  the  top  of  the  line  A,  as 
the  distance  the  body  falls  the 
first  second,  equal  to  |  g. 
Measure  from  B  twice  this  dis- 
tance to  represent  the  velocity 


Sfor2Bec.=4(is/) 


Sfor3sec.=9(ij/) 


Sfor4nec.=16(i0r)    — 


v=4g 


Sfor58ec.=25(i0)    _ 


v=5ff 


S  for  6  Bec.=36  (J  g) 


s  in  1st  sec.=l  (|  g) 
s  in  2d  sec.=3  (J  g) 

s  in  3d  sec.=5  (J  g) 
t  in  4th  sec.=7  (J  g) 

s  in  5th  sec.=9  (|  g) 
s  in  6th  8ec.=ll  ()  g) 


FIG.  14 


44  THE  MECHANICS  OF  SOLIDS 

gained  during  the  first  second.  Make  this  a  heavy  line  and 
extend  a  light  line  to  C,  a  point  J  g  farther  on.  Then  BC 
will  be  made  up  of  two  parts,  one  of  which  represents  the 
distance  passed  over  because  of  the  velocity  gained  during 
the  first  second,  and  the  other  the  additional  distance  the 
body  falls  because  of  gravity  acting  on  it  for  the  second 
second.  Points  D,  E,  etc.,  may  be  found  in  a  similar  manner. 

43.  Initial  Velocity.  —  If  a  body  is  thrown  vertically  down- 
ward, its  velocity  and  the  space  passed  over  in  any  time  will 
differ  from  those  of  a  falling  body  that  starts  from  a  condi- 
tion of  rest.  If  we  let  V  represent  the  velocity  per  second 
of  such  a  body  at  the  beginning,  we  may  write 

Velocity  per  second  at  the  end  of  1  sec.  ='V-\-g, 
Velocity  per  second  at  the  end  of  2  sec.  =  V  +  2  g, 
Velocity  per  second  at  the  end  of  3  sec.  =  V  +  3  g, 
Velocity  per  second  at  the  end  of  t  sec.    =  V  +  tg, 
or  x=v  +  gt,  (10) 

a  formula  that  differs  from  Formula  7  only  in  supposing 
an  initial  velocity.  An  initial  velocity  makes  correspond- 
ing changes  in  Formulas  8  and  9  also,  and  they  become 

s=  F+J0(2<-1),  (ii) 

and  8  =  Vt  +  %gt2.  (12) 


44.  Projectiles.  —  (a)  Bodies  thrown  Horizontally.  —  The 
path  of  a  projectile  may  be  obtained  by  combining  the  uni- 
form motion  due  to  the  impulsive  force  with  the  motion 
due  to  the  force  of  gravity  ;  and  since  gravity  is  a  constant 
force,  the  body  will  generally  move  in  a  curved  path.  The 
path  of  a  body  thrown  horizontally  may  be  constructed 
graphically  as  follows  (neglecting  the  resistance  of  the  air). 


MOTION,  VELOCITY,  AND   FORCE 


45 


Take  the  axes  as  in  Fig.  15.  Let  .r  represent  horizontal  motion 
and  y  vertical  motion.  Suppose  the  horizontal  velocity  is 
50  ft.  per  second.  Compute 
the  values  of  S  from  the  for- 
mula S  =  J  gP,  and  determine 
the  position  of  the  projectile 
at  the  end  of  each  second. 
A  curve  joining  the  positions 
will  represent  the  path  re- 
quired ;  if  the  page  is  held  in  a 
vertical  plane,  the  curve  is  the 
path  in  miniature.  This  curve 
is  of  the  form  called  parabolic. 

Demonstration.  —  Fix  a  sheet 
of  cross  section  paper  to  the  ap- 
paratus shown  in  Fig.  16  by  the 
clips  on  the  board  and  fasten  a 
sheet  of  carbon  tracing  paper  in  contact  with  it.  Project  a  steel 
ball  from  its  support  and  it  will  roll  down  the  inclined  plane. 

Remove  the  tracing 
paper  and  note  the 
relation  between  the 
horizontal  and  ver- 
tical velocities. 
Change  the  inclina- 
tion of  the  plane 
and  repeat. 

(b)  Bodies  thrown  Verti- 
cally Upward.  —  When  a 
body  is  rising  against  the 
force  of  gravity,  the  loss 

in  its  velocity  is  the  same  as  its  gain  in  velocity  when 
falling;    i.e.,  32.16  ft.  per  second,  if  we  neglect  the  resist- 


FIQ.  15 


46  THE   MECHANICS  OF  SOLIDS 

ance  of  the  air.  The  body  is  said  to  have  a  negative  ac- 
celeration, i.e.,  its  velocity  is  uniformly  diminishing  and  its 
final  velocity  is  zero.  Hence  if  a  body  is  thrown  vertically 
upward  with  a  velocity  of  64.32  ft.  per  second,  it  rises  for 
2  sec.,  when  its  velocity  becomes  zero  and  it  begins  to  fall. 
It  then  falls  for  2  sec.,  and  reaches  the  ground  with  its  origi- 
nal velocity  of  64.32  ft.  per  second.  The  time  during 
which  a  body  will  rise  when  thrown  vertically  upward  may 

be  expressed  by  the  formula  t  =  -., 

g 

(c)  Bodies  thrown  at  an  Angle.  —  When  a  body  is  thrown 
at  an  angle,  the  velocity  with  which  it  is  thrown  in  any 
direction  may  be  considered  a  velocity  of  which  the  horizontal 
and  vertical  velocities  are  components.  If  in  Fig.  17  AB 
represents  the  velocity  with  which  a  ball  is  thrown,  the  com- 
ponents AC  and  AD  will  represent  the  horizontal  and  verti- 
cal velocities  respectively.  The  angle  BAC  is  the  angle  of 
elevation,  and  the  distance  AE  is  the  range.  In  the  foregoing 

cases  no  allowance 
was  made  for  the 
resistance  of  the  air, 
but  its  effect  upon 

FIG.  17  E 

the  form  of  the  path 
in  this  case  is  shown -in  Fig.  17.  Its  effect  is  to  lessen  both 
velocities  (horizontal  and  vertical)  by  an  amount  which  is 
much  greater  for  high  velocities  than  for  low  ones.  Show 
what  its  effect  would  be  in  cases  a  and  b  of  this  section. 

The  path  ABE  is  called  the  trajectory  and  is  similar  in 
shape  to  that  of  a  batted  baseball.  The  trajectory  of  a  rifle 
ball  is  much  flatter  on  account  of  the  high  speed  of  the  pro- 
jectile. One  advantage  of  smokeless  over  black  powder  is 
that  it  gives  a  flatter  trajectory. 


MOTION,  VELOCITY,  AND   FORCE  47 

45.  Momentum.  —  The  product  of  the  mass  of  a  body  by 
its  velocity  is  called  its  momentum,  or  quantity  of  motion. 
In  the  C.  G.  S.  (centimeter-gram-second)  system  (§  28)  the 
unit  of  momentum  is  the  bole,  i.e.,  the  momentum  of  1  g. 
of  matter  moving  with  a  velocity  of  1  cm.  per  second.      The 
expression  b  =  Mv  (13) 

is  the  formula  for  momentum.  There  is  no  name  for  the 
unit  in  the  F.  P.  S.  (foot-pound-second)  system,  but  the 
unit  would  be  practically  the  momentum  of  1  Ib.  moving 
at  the  rate  of  1  ft.  per  second.  A  ferryboat  moving  slowly 
has  great  momentum,  as  is  shown  when  it  strikes  the  side 
of  the  slip.  Why? 

46.  Force  may  be  defined  as  that  which  tends  to  produce, 
to  change,  or  to  destroy  the  motion  of  a  body,  that  is,  to 
change  its  momentum.     Forces  may  be  measured  by  the 
velocities  imparted  in  the  unit  of  time,  to  the  masses  upon 
which  they  act ;  hence  the  equation  for  a  force  is 

Force  =  Mass  X  Acceleration, 

or  '   F  =  Ma,  (14) 

or,  since  v  =  at,  Ft  =  Mv. 

47.  The  Absolute  Unit  of  Force,  in  the  C.  G.  S.  system,  is 
the  dyne.     This  is  the  force  that,  acting  upon  1  g.  of  mass, 
will  give  to  it  an  acceleration  of  1  cm.  per  second  per  second. 

Since  the  dyne  is  a  very  small  unit,  it  is  sometimes  convenient 
to  use,  instead,  the  megadyne,  equal  to  1,000,000  dynes. 

In  the  F.  P.  -S.  system  the  absolute  unit  of  force  is  the 
poundal,  which  is  the  force  that  by  pushing  against  1  Ib.  of 
matter  will  give  to  it  an  acceleration  of  1  ft.  per  second  per 
second. 


48  THE   MECHANICS  OF  SOLIDS 

The  formula  F  =  Ma  refers  to  absolute  units ;  it  means 


No.  of  abso- 
lute units  of 
force 


No.  of  units 
of  mass  (g. 
or  Ib.) 


No.  of  units  of  length 
in  acceleration  per  sec. 
per  sec.  (cm.  or  ft.) 


•For  instance,  to  measure  a  force  that  gives  to  a  mass  of 
6  g.  an  acceleration  of  5  cm.  per  second  per  second,  we  write 
F  =  Ma  =  6  X  5  =  30  dynes.  Again,  to  determine  the 
weight  of  a  1 -pound  mass  at  New  York,  or  the  force  by  which 
a  mass  of  1  pound  is  pulled  downward  by  gravity  there,  we 
observe  that  a  freely  falling  body  at  New  York  has  an  accelera- 
tion of  980.2  cm.  or  32.16  ft.  per  second  per  second.  Hence 
in  this  case  F  =  I  X  32.16  =  32.16  poundals. 

Since  the  dyne  gives  to  one  gram  of  matter  an  acceleration 
of  1  cm.  per  second  per  second  and  gravity  acting  on  this  same 
gram  gives  it  an  acceleration  of  980.2  cm.,  the  weight  of 
1  gram  =  980.2  dynes.  The  force  of  gravity  varies  a  little 
at  different  points  on  the  earth's  surface.  But  if  we  let  g 
represent  the  acceleration  due  to  gravity,  and  W  the  weight 
expressed  in  absolute  units  of  force,  the  formula 

W  =  Mg,  or  M  =  —  •  (15) 

will  hold  true  for  any  place  whatever. 

48.  The  Gravity  Unit  of  Force.  —  Instead  of  using  abso- 
lute units,  we  may  measure  forces  by  comparing  them  with 
the  weight  of  a  standard  mass.  A  force  of  1  pound,  for  in- 
stance, means  a  force  equal  to  the  force  by  which  a  mass  of 
1  pound  is  pulled  downward  by  gravity.  The  pound,  as  a 
gravity  unit  of  force,  is  therefore  equal,  at  New  York,  to 
32.16  poundals ;  and  the  gram  to  980.2  dynes.  As  the  force 
of  gravity  varies  at  different  places,  the  gravity  unit  of  force 


MOTION,  VELOCITY,  AND  FORCE  49 

is  variable.  The  pound,  nowever,  everywhere  equals  g 
poundals,  and  the  gram  everywhere  equals  g  dynes. 

By  combining  Equations  14  and  15  we  obtain  the  formula 

F  =  ^  (16) 

9 

in  which  W  is  the  weight  of  the  body  moved.  If  W  is  ex- 
pressed in  absolute  units  .(=  Mg),  the  result  F  will  be  ex- 
pressed in  absolute  units  ;  but  if,  as  is  usual,  W  is  expressed 
in  gravity  units  (=  M),  then  F  will  be  expressed  in  gravity 
units. 

For  instance,  to  measure  the  force  that  will  be  required  at  New 
York  to  impart  in  one  second  a  velocity  of  20  feet  per  second  to  a 
mass  of  160  pounds,  we  write 

„      Wa      160  X  20 


49.  Newton's  Laws  of  Motion.  —  As  a  result  of  his  investi- 
gation in  mechanics,  Sir  Isaac  Newton  formulated  the  follow- 
ing laws  : 

I.  Every  body  tends  to  persevere  in  its  state  of  rest  or  of 
uniform  motion  in  a  straight  line,  unless  it  is  acted  on  by  an 
impressed  force. 

II.  Change  of  momentum  is  proportional  to  the  impressed 
force  and  takes  place  in  the  direction  of  the  straight  line  in  which 
the  force  acts. 

III.  To  every  action  there  is  always  an  equal  and  contrary 
reaction. 

50.  Newton's  First  Law.  —  If  a  body  is  left  in  a  certain 
place,  and  after  an  interval  it  is  not  found  there,  we  under- 
stand at  once  that  it  has  been  removed,  that  some  force  has 
been  brought  to  bear  upon  it.     If,  however,  a  body  is  in 

Rev. 


50  THE  MECHANICS  OF  SOLIDS 

motion,  we  cannot  prove  by  actual  experiment  that  it  tends 
to  go  on  in  the  same  straight  line,  as  the  law  states,  because 
it  is  not  possible  to  remove  all  resistances  to  a  moving  body, 
and  these  resistances  are  forces.  But  if  the  resistances  are 
made  as  little  as  possible,  the  motion  continues  much  longer. 
If  a  ball  is  rolled  first  on  the  ground,  then  on  a  floor,  and  then 
on  smooth  ice,  with  the  same  force  each  time,  the  effect  of 
the  reduced  resistance  is  each  time  shown  in  the  increased 
distance  to  which  the  ball  rolls. 

51.  Newton's  Second  Law  means  that  any  force  acting 
upon  a  body  produces  its  own  effect,  whether  acting  alone  or 
in  conjunction  with  other  forces. 

This  does  not  mean  that  if  a  motor  boat,  for  example, 
starts  directly  across  a  river,  it  will  land  at  the  same  point 
as  it  would  if  there  were  no  current,  but  it  does  mean  that 
the  work  done  by  the  motor  will  carry  the  boat  across  the 
stream  just  as  though  there  were  no  current 
flowing. 

52.  Verification  of  Newton's  Second  Law.  — 
When  a  body  is  dropped,  it  falls  in  a  vertical 
line  with  a  uniformly  increasing  velocity  due 
to  the  constant  force  of  gravity.  If  instead 
of  being  dropped  it  is  struck  a  blow,  it  moves 
in  a  curved  path,  the  resultant  of  the  uniform 
motion  due  to  the  blow  and  the  accelerated 
motion  due  to  gravity.  According  to  New- 
ton's Second  Law,  the  time  of  falling  should 
be  the  same  in  both  cases  if  the  blow  is  given 
horizontally. 


^^MHHBp!! 


Demonstration.  — A  simple  form  of  apparatus  for 
FIG.  18          the  demonstration  of  this  law  is  shown  in  Fig.  18. 


MOTION,  VELOCITY,   AND  FORCE  51 

A  support  carries  near  the  top  a  shelf  with  a  hole  in  it.  A  thin 
wooden  strip,  fixed  at  the  upper  end,  comes  vertically  down  above 
the  hole  in  the  shelf.  Place  a  small  ball  or  marble  on  each  side  of 
the  strip,  so  that  the  one  over  the  hole  is  suspended  by  pressure 
between  the  wooden  strip  and  a  cleat  on  the  shelf.  Let  the  ham- 
mer fall  upon  the  strip,  and  one  ball  will  be  thrown  out  horizon- 
tally and  the  other  dropped  vertically. 

53.  Newton's  Third  Law  is  only  a  statement  of  what  we 
are  familiar  with,  as  reaction.  If  a  cup  is  struck  against  the 
edge  of  a  table,  the  table  reacts  against  the  cup  and  breaks 
it.  An  ocean  steamship  is  pushed  along  by  the  reaction  of 
water  against  the  blades  of  the  screw  propeller.  If  a  swimmer 
attempts  to  dive  from  a  springboard,  he  makes  use  of  both 
the  elasticity  and  the  reaction  of  the  board.  In  order  to 
jump  far  a  boy  must  stand  on  something  fixed,  so  that  it 
shall  react  against  the  push  of  his  muscles.  If  he  should 
attempt  a  long  jump  while  standing  upon  the  seat  of  a  swing, 
he  would  only  succeed  in  se.tting  the  swing  in  motion  and 
getting  a  fall. 

Demonstration.  —  The  action  and  reaction  of  elastic  balls  can  be 
shown  by  means  of  a  grooved  board.  Place  a  single  ball  in  the 
groove  and  then  drive  a  second  ball  against  it  with  the  end  of  a 
stick.  The  moving  ball  will  stop  as  soon  as  it  strikes  the  one  that 
is  standing  still,  while  that  one  will  move  on  with  the  velocity  of  the 
first.  Why? 


FIG. 19 


With  a  half  dozen  balls,  a  number  of  combinations  of  stationary 
and  moving  balls-may  be  made  that  will  be  helpful  in  understanding 
the  significance  of  this  law  (Fig.  19). 


52  THE   MECHANICS  OF  SOLIDS 

The  "  Oscillator  "  electric  fan  is  an  example  of  the  practical  use  of 
reaction.  In  this  fan  a  circular  disk  is  carried  at  the  end  of  a  rod 
which  is  so  pivoted  to  the  support  of  the  fan  that  the  disk  can  be 
swung  from  one  side  of  the  fan  to  the  other. 
When  the  disk  is  on  one  side,  as  shown, 
the  reaction  of  the  air  upon  the  blades  of 
the  fan  is  partly  counterbalanced  by  the 
blowing  of  the  current  of  air  upon  the  disk. 
The  reaction  on  the  other  side  of  the  fan, 
not  being  counterbalanced,  pushes  the 
blades  on  that  side  backward,  and  the  fan 
support  turns  on  a  vertical  axis  carried  by 
the  standard.  When  the  fan  has  moved  a 
certain  distance,  a  pin  connected  with  the 
FIG.  20.— Oscillator  Fan  disk  rod  strikes  a  stop  placed  on  the  base, 
and  the  disk  is  swung  to  the  other  side  of 

the  fan.  The  turning  of  the  fan  is  now  reversed,  and  it  moves 
around  until  the  projecting  pin  strikes  a  second  stop,  when  a 
reversal  again  takes  place.  In  this  way  an  automatic  distribution 
of  the  air  current  over  a  room  is  secured. 

54.  Graphical  Representation  of  Forces.  —  If  the  motion  of 
a  body  is  that  imparted  by  a  single  force,  its  path  will  be 
rectilinear,  and  may  be  represented  by  a  straight  line.     The 
elements  of  a  force  are  :  (a)  its  point  of  application ;  (6)  its 
direction ;  (c)  its  magnitude.     The  force  may  be  represented 
by  a  line  beginning  at  the  point  of  application,  and  extending 
in  the  direction  in  which  the  force  acts,  to  a  distance  which 
is  a  measure  of  its  magnitude.     This  means  that  all  lines 
representing  magnitudes  must  be  drawn  to  the  same  scale. 

The  direction  of  the  motion  of  a  body  or  of  the  action  of 
a  force  is  indicated  by  placing  on  the  line  the  point  of  an 
arrow.  Such  lines  are  called  vector  lines,  or  vectors. 

55.  Composition  of  Forces.  —  When  two  forces,  having 
the  same  point  of  application,  act  at  the  same  time  upon 


MOTION,  VELOCITY,  AND  FORCE  53 

a  body,  we  can  imagine  some  one  force,  called  the  resultant, 
that  would  have  the  same  effect  as  the  two  actual  forces, 
which  are  called  components.  The  direction  and  intensity 
of  this  resultant  force  may  be  found  as  follows : 

(a)  When  the  forces  act  in  the  same  direction.  —  Suppose 
two  forces  act  upon  a  body,  tending  to  move  it  toward 
the  'east.  Let  one  of  them  be  a  force  of  2  dynes  and  the 
other  of  3  dynes.  Select  a  point  A  as  the  position  of  the 

A B  c D ^ 

FIG.  21 

body.  Draw  a  line  Ax  (Fig.  21)  to  represent  the  direction 
in  which  the  forces  act.  Take  any  convenient  scale  and  lay 
off  AB  to  represent  2  dynes,  and  AC  to  represent  3  dynes. 
Since  the  forces  AB  and  AC  are  acting  upon  the  same  body 
at  A  and  along  the  same  line,  Ax,  and  since  each  force  pro- 
duces its  own  effect,  their  resultant  must  be  equal  to  the  sum 
of  AB  and  AC;  hence  it  will  be  the  force  AD,  representing 
5  dynes. 

The  resultant  of  two  forces  acting  in  the  same  straight  line, 
in  the  same  direction,  is  the  sum  of  the  given  forces. 

(6)  When  the  forces  act  in  opposite  directions.  —  Suppose 
the  two  forces  to  act,  one  toward  the  east  and  the  other 


FIG.  22 

toward  the  west,  as  in  Fig.  22.  It  is  evident  that  the  force 
AB  will  act  against  AC,  and  that  the  resultant  will  be  AD, 
their  difference. 

The  resultant  of  two  forces  acting  in  the  same  straight  line, 
but  in  opposite  directions,  is  the  difference  of  the  given  forces 
and  acts  in  the  direction  of  the  greater.  It  two  equal  forces 


54 


THE  MECHANICS  OF  SOLIDS 


FIG.  23 


act  upon  a  body  in  opposite  Directions,  their  resultant  will 
be  zero,  the  forces  will  be  in  equilibrium,  and  the  body  will 
be  at  rest. 

(c)  When  the  forces  act  at  an  angle  to  each  other.  —  THE 
PARALLELOGRAM   OF  FORCES.  —  (1)   Suppose  the   force   P 

c  O^g-  23),  of  3  dynes,  to  act  toward 
the  east,  at  a  right  angle  to  the  force 
Q,  of  2  dynes,  acting  toward  the  south. 
Represent  P  by  AC,  and  Q  by  AB. 
Complete  the  parallelogram  by  draw- 
ing the  dotted  lines  BD  and  CD  (par- 
allel to  AC  and  AB,  respectively), 

and  their  intersection  will  locate  the  point  D  and  determine 

both   the   magnitude   and   the  direction  of  the  resultant, 

AD.     For  D  is  the  only  point  that  is  as  far  east  as  C  and 

as  far  south  as  B. 

In  each  figure  all  lines  representing  forces  must  be  measured 

by  the  same  scale. 

(2)  Suppose  the  force  Q  to  act  at  an  angle  CAB  to  the 

force  P  (Fig.  24).     Complete  the  parallelogram  to  determine 

the  point  D.     Then,  for  reasons  similar 

to  the  above,  AD  or  R  will  be  the  re- 
sultant required. 

The  resultant  of  any  two  forces  acting 

at  an  angle  to  each  other  may  be  found 

by  completing  the  parallelogram  upon  the 

forces  as  sides  and  drawing  the  diagonal 

from  the  common  point  of  application. 

(d)  When  there  are  more  than  two  forces.  —  The  resultant 
of  any  number  of  forces  can  be  found  by  a  repetition  of  the 
parallelogram  of  forces.     Suppose  three  forces,  P,  Q,  and  S 
(Fig.  25),  to  be  acting  on  a  body  at  A.    Complete  the  paral- 


FIQ.  24 


MOTION,  VELOCITY,  AND  FORCE 


FIG.  25 


lelogram  ACDB ;  then  AD  or  Rf  will  be  the  resultant  of  P 
and  Q.  Find  the  resultant  of  S  and  R'  by  completing  the 
parallelogram  AD  HE  • 
then  AH  or  R  will  be 
the  resultant  of  P,  Q, 
and  5. 

56.  Equilibrant—  The 
equilibrant  of  any  num- 
ber of  forces  is  a  force 
equal  in  magnitude,  and 
opposite  in  direction,  to 
their  resultant.  If  the  forces  and  their  equilibrant  act  upon 

a  body,  the  equilibrant  will 
counteract  the  other  forces, 
and  the  body  will  remain  at 
rest.  This  condition  is  shown 
in  Fig.  26,  in  which  the  equili- 
brant E  and  the  forces  P  and 
Q  keep  the  body  A  at  rest. 

57.  Verification  of  the  Par- 
allelogram of  Forces.  —  Dem- 
onstration. —  A  and  B  (Fig.  27)  are 
two  hooks  at  the  top  of  a  black- 
board. To  these  attach  two  spring 
balances,  C  and  D.  Hook  these  to 
the  ends  of  a  cord  to  which  a  second 
cord  is  tied  at  H.  Suspend  a 
weight  W  from  this  cord,  and  the 
point  H  will  be  kept  in  equilibrium 
by  the  three  forces.  The  resultant 
of  the  pulls  exerted  by  the  bal- 
ances C  and  D  may  be  found  as 
follows.  Mark  the  position  of  H  FIG.  27 


FIG.  26 


56 


THE  MECHANICS  OF  SOLIDS 


FIG.  28 


on  the  blackboard  and  the  direction  of  the  lines  leading  to  C  and  D. 
Take  He  to  represent  the  reading  of  the  balance  C,  and  on  the 
same  scale  lay  off  Hd  to  represent  the  reading  of  the  balance  D. 
Complete  the  parallelogram,  and  Hk,  the  resultant,  will  be  found 
to  represent  an  amount  equal  to  W,  the  equilibrant,  and  to  be 
vertical. 

68.  Forces  not  Lying  in  the  Same  Plane. — When  three 
forces  having  the  same  point  of  application  do  not  lie  in  the 

same  plane,  the  resultant 
is  the  diagonal  of  the 
parallelepiped  formed  on 
these  forces  as  edges. 
Suppose  the  three  forces 
are  P,Q,  and  S  (Fig.  28). 
The  resultant  of  P  and 
Q  is  R'  in  the  plane 
ABEC,  while  the  diagonal  AH  is  the  resultant  of  Rf  and 
S  in  the  plane  AEHD,  and  is  the  required  resultant. 

69.  Resolution  of  Forces.  —  In  the  composition  of  forces 
we  have  given  the  component  forces  to  find  the  resultant, 
while  in  the  resolution  of  forces  the  resultant  is  given  and 
the  components  are  to  be  found.     When  two  components 
are  to  be  found,  the  problem  is  to  construct  a  parallelogram 
on  the  resultant  as  the  diagonal,  such  that  the  desired  com- 
ponents will  be  sides  of  the  parallelogram.     There  are  several 
cases   of  this   problem,  of  which   the 

following  are  the  most  important : 

(a)  Given,  the  resultant  and  one  of 
two  components,  to  find  the  other 
component  (Fig.  29).  Suppose  the 
force  P  and  one  of  its  components  Q 
are  given,  and  it  is  required  to  find  the  FIG.  29 


B 


MOTION,  VELOCITY,  AND  FORCE 


57 


FIG.  30 


other  component.  Complete  the  parallelogram  on  P  as 
the  diagonal  and  Q  as  one  side  (by  connecting  B  and  E,  and 
drawing  ED  parallel  to  BA,  and  AD 
parallel  to  BE).  Then  C  will  be  the 
required  component. 

(6)  Given,  the  resultant  and  the  direc- 
tion- of  each  of  two  components,  to  find 
the  components.  Let  AB  (Fig.  30)  be 
the  given  resultant  and  AC  and  AD  the 
directions  of  the  required  components. 
From  B  draw  two  lines,  one  parallel  to 
AD  and  the  other  parallel  to  AC.  Their 
intersections  with  AC  and  AD  will  determine  the  points 
E&ndF;  and  AE  and  AF  will  be  the  required  components 
of  AB. 

60.  General  Condition  of  Equilibrium.  —  So  far  we  have 
considered  only  motion  of  translation,  or  motion  in  which 
all  the  parts  of  the  moving  body  move  in  the  same  direction 
and  with  the  same  speed.     But  there  may  also  be  a  motion 
of  rotation,  as  when  a  body  turns  on  an  axis.     In  rotation, 
parts  of  the  body  on  opposite  sides  of  the  axis  move  at  any 
instant  in  opposite  directions ;  and  each  part  moves  contin- 
uously in  a  curved  path,  with  a  speed  that  varies  with  its 
distance  from  the  axis.     In  order  to  have  complete  equilibrium, 
not  only  must  the  resultant  of  all  the  forces  tending  to  produce 
translation  of  the  body  be  zero,  but  the  resultant  of  all  the  forces 
tending  to  produce  rotation  must  also  be  zero. 

61.  The  Moment  of  a  Force.  —  Suppose  there  are  two 
forces,  F  and  F' ,  acting  at  right  angles  to  the  bar  AB,  each 
tending  to  rotate  it  about  the  pivot  C  (Fig.  31).     It  is  evident 
that  the  tendency  of  each  force  to  produce  rotation  depends 


58 


THE   MECHANICS  OF  SOLIDS 


d' 


FIG.  31 


not  only  upon  the  magnitude  of  the  force,  but  also  upon  its 
distance  from  the  point  (7,  about  which  it  tends  to  turn  the 
bar.  If  the  distance  CA  is  d,  and  CB 
is  d',  the  tendency  to  produce  rotation 
exerted  by  F  is  proportional  to  the 
product  Fd,  which  is  called  the  moment 
of  the  force  F ;  so,  too,  the  moment  of 
the  force  Ff  is  F'd'.  The  point  (7, 
about  which  the  rotation  takes  place, 

is  called  the  center  of  moments.  The  force  F'  tends  to  pro- 
duce a  clockwise  and  the  force  F  a  counterclockwise  rota- 
tion around  the  point  C. 

If  the  forces  F  and  F'  d>- 

do  not  act  in  a  direction 
that  is  perpendicular  to 
the  bar  AB,  as  in  Fig. 
32,  then  the  distances  d 
and  d'  will  not  be  CA 
and  CB,  but  CD  and 
CE,  which  are  the  per- 
pendiculars drawn  from  C  to  the  directions  of  the  forces. 
The  moment  of  a  force  is  the  product  of  the  force  by  the 
p  perpendicular  distance 

from  the  center  of  mo- 

R ^    ments  to  the  direction  of 

the  force. 


FIG.  32 


FIG.  33 


62.  Parallel   Forces 

are  two  or  more  forces 
that  act  upon  a  body 

in  parallel  directions  but  at  different  points  of  application. 

Suppose  two  parallel  forces,  P  and  Q  (Fig.  33),  are  acting 


MOTION,   VELOCITY,  AND  FORCE  59 

upon  a  rigid  bar  at  the  points  A  and  B.  Then  the  result- 
ant, not  only  as  regards  translation  but  also  with  respect 
to  rotation  about  any  point  in  the  bar,  will  be  equal  to  the 
sum  of  the  forces  in  magnitude,  and  parallel  to  them  in 
direction,  and  will  be  applied  at  a  point  C,  between  A  and 
B,  such  that  BC :  AC  =  P:Q.  The  equilibrant  will  also 
be  applied  at  C,  and  is  equal  to  R  in  magnitude  and  op- 
posite to  it  in  direction.  This  means  that  whenever  three 
parallel  forces  are  in  equilibrium,  one  of  them  is  between  the 
other  two,  is  equal  to  their  sum,  and  is  opposite  them  in  di- 
rection. Since  the  moment  of  P  equals  the  moment  of 
Q,PXAC=QX  BC,  from  which  the  distance  of  C  from 
either  A  or  B  can  be  found. 

Demonstration.  —  The  truth  of  the  above  equation  for  deter- 
mining the  point  of  application  may  be  verified  by  suspending  from 
a  meter  stick  two  weights,  P  and  Q, 
and  supporting  the  stick  and  its 
load  by  a  spring  balance  or  scale,  as 
in  Fig.  34.  The  weights  can  be 
supported  from  the  meter  stick  by 
cords  with  loops  passing  over  the 
stick,  and  the  position  of  the  scale 
can  be  found  by  slipping  the  loop 
to  which  it  is  attached  along  the 
stick  until  the  stick  balances  in 

a  horizontal  direction.  Before  the  proportion  P:Q  =  BC :  AC  is 
tested,  a  small  weight  should  be  suspended  from  the  short  end  near 
A  so  that  the  stick  will  balance  when  the  weights  P  and  Q  are  re- 
moved. The  scale  will  read  not  only  the  sum  of  P  and  Q,  but  the 
weight  of  the  stick  and  small  weight  also. 

The  application  of  this  principle  is  useful  in  determining  the 
pressure  upon  the  abutments  of  a  bridge  when  a  load  is  pass- 
ing over  it.  If  a  train  passes  over  the  bridge,  the  pressures 


60 


THE  MECHANICS  OP  SOLIDS 


upon  the  abutments  (in  addition  to  the  weight  of  the  bridge) 
are  constantly  varying  from  the  whole  weight  to  zero,  and 


FIG.  35.  —  Bridge  across  the  Niagara  River 

vice  versa,  while  the  sum  of  the  two  pressures  is  equal  to 
the  weight  of  the  train  (Fig.  35). 

The  resultant  of  any  number  of  parallel  forces-  can  be  found 
by  finding  first  the  resultant  of  two  of  them,  then  combining 
this  resultant  with  a  third  force  to  find  their  resultant,  and 
so  on.  Any  number  of  parallel  forces  are  in  equilibrium 
when  the  resultant  of  all  the  forces  in  one  direction  is  equal 
to  and  has  the  same  point  of  application  as  the  resultant  of  all 
the  forces  in  the  opposite  direction. 

63.  Couples.  —  The  parallel  forces  P  and  Q  shown  in 
Fig.  33  can  be  replaced  by  a  single  force,  R,  or  counter- 
balanced by  a  single  force,  E.  Parallel  forces,  however,  can 
be  applied  to  a  body  in  such  a  way  that  neither  of  these  things 
can  be  done.  If  the  parallel  forces  are  equal  and  in  opposite 


MOTION,   VELOCITY,   AND   FORCE 


61 


directions,  their  resultant  is  zero  so  far  as  motion  of  transla- 
tion is  concerned,  but  they  tend  to  turn  the  bar  AB  (Fig.  36) 
into  the  position  shown  by  the 
dotted  lines.  This  combination 
of  forces  is  called  a  couple  and 
produces  rotation  only. 

64.  The  Graphical  Represen- 
tation and  Composition  of  Ve- 
locities. —  Any  velocity  of  which  the  starting  point,  the 
rate,  and  the  direction  are  known  can  be  represented  graph- 
ically by  a  vector  line  (§  54). 

If  the  directions  of  two  component  velocities  are  in  the 
same  straight  line,  the  resultant  velocity  is  either  the  sum 
or  the  difference  of  the  two  velocities.  A  person  walking 
through  a  railway  train  from  the  rear  to  the  front  has  a  greater 
velocity  with  respect  to  the  earth  than  a  person  sitting  in  a 
seat,  while  a  person  walking  from  the  front  to  the  rear  has  a 
smaller  velocity. 

If  the  directions  of  two  component  velocities  are  not  in  one 
straight  line,  the  resultant  velocity  can  be  found  by  combin- 
ing the  velocities  as  forces  are  combined  in  the  parallelogram 
of  forces.  For  example,  if  a  man  rows  a  boat  across  a  stream 
with  a  uniform  velocity  of  2  miles  per 
hour  while  the  stream  flows  with  a 
uniform  velocity  of  1.5  miles  per  hour, 
the  direction  taken  by  the  boat  will 
be  determined  by  these  velocities  in- 
dependently of  the  width  of  the 
stream.  If  the  boat  starts  from  A, 
Fig.  37,  the  direction  of  the  path  will  be  found  by  laying 
off  AB  to  represent  the  velocity  of  2  miles  per  hour  and 


FIG.  37 


62  THE  MECHANICS  OF  SOLIDS 

AC  at  a  right  angle  to  it  to  represent  a  velocity  of  1.5  miles 
per  hour;  then  AD  will  be  the  direction  the  boat  will 
take.  If  the  width,  AE,  of  the  stream  is  known,  the 
length  of  the  path,  AF,  is  easily  determined. 

A  velocity,  as  well  as  a  force,  can  also  be  resolved  into  com- 
ponents, as  in  §  59. 

65.  Reflected  Motion.  —  If  an  elastic  ball  strikes  against 
a  fixed  body,  it  will  rebound.     This  is  called  reflected  motion, 
and  is  caused  by  the  reaction  of  the  body  against  which  it 
strikes.     If  a  moving  body  is  not  elastic,  the  reaction  of  the 
body  against  which  it  strikes  will  flatten  it,  as,  for  example, 
when  a  ball  of  putty  is  dropped  upon  the  floor.     If  both 
the  bodies  are  highly  elastic,  the  direction  of  the  rebound 
will  be  such  that  the  angle  of  reflection  will  equal  the  angle 

of  incidence.  This  is  the  Law 
of  Reflection,  and  may  be  veri- 
fied as  follows : 

Demonstration.  —  Place  a  strip 
of  board  on  its  edge  upon  a  table 
resting  against  the  wall.  Roll  an 
elastic  ball  across  the  table  along 

— •^•HBBBMHBMBM       the  line  AB  (Fig.  38)  against  the 

board.  From  B,  where  the  ball 
strikes,  draw  BD  perpendicular  to 

FJG  38  the  board-     Then  the  an8le  CBD> 

the    angle  of    reflection,    will  be 

found  equal  to  the  angle  ABD,  the  angle  of  incidence.  (The  path 
of  the  ball  can  be  readily  traced  by  dusting  the  table  with  crayon 
dust.) 

66.  Curvilinear  Motion.— The  path   of  a  body    whose 
motion  is  that  imparted  by  a  single  impulsive  force  is  rec- 
tilinear.    If  its  motion  is  due  to  two  impulsive  forces  that 
have  acted  upon  it,  its  path  will  still  be  rectilinear;  but  if 


MOTION,   VELOCITY,  AND  FORCE 


63 


the  motion  due  to  an  impulsive  force  is  combined  with  that 
due  to  a  constant  force,  not  acting  in  the  same  straight  line, 
its  path  will  be  curvilinear.  If  a 
stone  is  tied  to  a  cord  and  swung 
around,  a  curved  path  is  the  re- 
sult. If  the  cord  should  break, 
the  -stone  would  go  off  in  a 
straight  line  —  the  tangent  line 
AE  (Fig.  39);  but  the  cord 
prevents  the  stone  from  taking 
such  a  course  and  compels  it  to  go  in  the  curved  path  ADE. 

67.  Centripetal  and  Centrifugal  Forces.  —  The  pull  of  the 
string  that  compels  the  body  in  Fig.  39  to  move  in  a  circular 
path  is  directed  toward  the  center,  C,  and  is  called  the  cen- 
tripetal force.  Since  this  force  acts  constantly  in  a  direction 
at  a  right  angle  to  the  direction  of  the  motion  of  the  body, 
it  does  not  affect  its  velocity,  but  does  give  it  an  acceleration 
towards  the  center.  The  reaction  that  the  moving  body 
offers  to  the  centripetal  pull  of  the  cord  is  called  the  cen- 
trifugal force  and  is  equal,  in  amount/  to  the  centripetal 
force.  If  part  of  the  cord  is  replaced  by  a  spring  scale,  its 
reading  will  be  a  measure  of  this  force,  which  depends  upon  the 
mass  of  the  body,  its  velocity,  and  the  radius  of  the  circle. 

The  acceleration  given  by  centripetal  force  is  equal  to 

— .     Since  force  equals  Ma  or  - — ,  the  expression  for  either 
centripetal  or  centrifugal  force  is 

'(17) 

or  t\  =  — .  (18) 


r 
Wv* 

9r 


For  proof  of  this  formula  see  Appendix. 


64 


THE   MECHANICS  OF  SOLIDS 


Equation  17  expresses  the  force  in  absolute  units,  and  Equa- 
tion 18  in  gravity  units. 

68.  Examples  of  Centrifugal  Force.  —  There  are  many 
examples  of  the  so-called  centrifugal  force.     In  every  case 

in  which  the  force 
that  holds  the  body 
to  the  center  is  over- 
come, the  body  flies 
off  in  a  direction  tan- 
gent to  the  curve. 
The  flying  of  mud 
from  a  carriage  wheel, 
the  bursting  of  a 
grindstone,  the  sep- 
aration of  the  milk 
from  the  cream  in  a 

FIG.  40. -Centrifugal  Extractor  dftipy    separatorj   the 

extraction  of  honey  from  the  comb  in  a  rotating  extractor, 
the  action  of  the  water  in  a  centrifugal  drying  machine,  are 
all  results  of  this  force.  It 
is  on  account  of  this  tend- 
ency that  a  race  course  is 
banked  to  make  the  out- 
side of  the  track  the  high- 
est, and  that  on  a  curve  of 
a  railroad  track  the  outer 
rail  is  made  higher  than 
the  inner  rail. 

In  the  governor  of  a  steam 
engine  two  weighted  arms 
hinged  to  a  vertical  shaft  fly 
apart  when  revolving  at  high  FIG.  41.— Extractor  Basket 


MOTION,   VELOCITY,  AND  FORCE 


65 


speed  and  fall  together  at  low  cpeed.  These  motions  control  the 
admission  of  steam  and  hence  the  speed  of  the  engine.  The  cen- 
trifugal drying  machine  or  extractor  (Fig.  40)  used 
in  laundries  consists  of  an  inner  copper  basket  that 
can  be  rotated  on  a  vertical  axis  at  high  speed. 
This  basket  (Fig.  41)  is  pierced  with  rows  of  holes 
along  its  circumference  through  which  the  water 
from  the  clothes  is  driven  by  centrifugal  force. 

Demonstration.  —  Attach  to  a  rotating  machine 
a  flattened  glass  globe,  suspending  it  as  in  Fig.  42. 
Pour  into  the  globe  some  mercury  and  colored 
water.  Put  the  machine  in  motion,  and  the  mer- 


FIG. 42 


\ 


c:; 


FIG.  43 


cury  will  form  a  ring 
around  the  globe  at  its 
greatest  diameter,  as 
at  A,  while  the  water 
will  form  a  second  ring 
\  inside,  between  B  and 

\     B'- 

Replace  the  globe  by 
the  objects  that  are 
shown  in  Fig.  43.  A  is  a 
wooden  disk  suspended 
from  the  edge;  B,  a 
wooden  cone  suspended 

from  the  apex ;   C,  a  loop  of-  small  chain ;  and  D,  a  rod  suspended 

from  one  end.    On  rotating  the  support  they  will 

all  tend  to  rotate  on  their  short  axes. 

69.  The  Gyroscope.  —  The  centrifugal 
force  of  a  rotating  body  gives  it  great  sta- 
bility of  position.  This  is  shown  by  the 
action  of  an  ordinary  top,  or  better  by  a 
gyroscope— a  wheel  with  a  heavy  rim  ro- 
tating on  an  axle,  the  ends  of  which  are 
pivoted  in  a  ring.  When  this  wheel  is  rotat- 
ing at  a  high  speed,  it  shows  a  strong  re- 
Rev. 


FIG.  44. — A  Simple 
Gyroscope 


66 


THE  MECHANICS  OF  SOLIDS 


FIG.  45. — :Brennan  One-rail  Car 
By  courtesy  of  The  Book  of  Knowledge. 


sistance  to  any  force  that  would  change  its  plane  of  rotation 
or  the  direction  of  its  axis.1      Advantage  is  taken  of  this 

gyroscopic  action  in 
the  placing  of  the 
flywheels  of  engines 
used  on  shipboard : 
they  are  so  located 
that  their  axes  ex- 
tend crosswise  of  the 
ship,  thus  tending 
to  reduce  the  side- 
wise  rolling  motion. 
In  a  Brennan  one- 
rail  car  (Fig.  45),  stability  is  secured  by  means  of  a  pair 
of  gyroscopic  wheels  rotating  in  opposite  directions,  with 
their  axes  extending  across  the  car. 

Questions 

1.  If  a  constant  force  acts  upon  a  body  at  rest  and 'gives  it  a 
velocity  of  10  ft.  per  second  in  5  sec.,  what  is  the  average  velocity 
of  the  body?     What  is  its  acceleration?     How  far  would  it  move  in 
the  next  5  sec.  if  it  neither  gained  nor  lost  velocity? 

2.  Suppose  an  automobile  to  start  from  rest  and  gain  a  velocity 
of  20  ft.  per  second  in  4  sec.     What  was  the  acceleration? 

3.  Why  does  a  loaded  auto  truck  start  more  slowly  than  an 
empty  one? 

4.  What  would  be  the  result  of  doubling  the  power  of  the 
engine  of  the  truck? 

5.  Suppose  both  the  load  and  power  of  the  engine  were  doubled. 
What  effect  would  it  have  upon  the  acceleration?    Why? 

1  If  the  axle  is  supported  at  one  end  only,  the  force  of  gravity  tends 
to  depress  the  other  end ;  but  the  gyroscopic  resistance  to  this  force 
produces,  instead,  a  slow  rotation  of  the  entire  instrument  about  the 
point  of  support,  with  a  nearly  constant  inclination  of  the  axis  to  a 
horizontal  plane. 


MOTION,   VELOCITY,  AND  FORCE  67 

6.  Why  does  the  truck  not  stop  as  soon  as  the  power  is  shut  off? 
What  means  are  employed  to  stop  it  ? 

7.  Does  the  water  pouring  over  a  high  fall  reach  the  ground  as 
soon  as  a  stone  dropped  from  the  top? 

8.  Why  does  it  require  a  harder  pull  to  draw  a  loaded  sled  up  a 
hill  than  along  a  level? 

9.  Suppose  two  boys  pull  on  a  rope  attached  to  the  hook  of  a 
spring,  scale,  the  ring  of  which  is  fastened  to  a  hook  in  the  wall. 
What  will  the  scale  read  if  one  boy  pulls  8  Ib.  and  the  other  12  Ib.  ? 

10.  Suppose  they  tic  one  rope  to  the  hook  of  the  scale  and  another 
to  the  ring  and  pull  in  opposite  directions,  one  pulling  exactly  8  Ib. 
as  in  problem  9,  and  the  other  pulling,  or  trying  to  pull,  12  Ib. 
Will  the  scale  move  and  what  will  it  read  ? 

11.  What  must  each  boy  pull  so  that  the  scale  will  not  move? 
How  much  will  it  then  read  ?   What  will  be  the  strain  upon  the  ropes  ? 

12.  Suppose  you  had  an  old  horse  and  a  young  horse  hitched  to  a 
load.     How  would  you  hitch  them  to  the  evener  so  that  the  young 
horse  would  have  to  pull  the  greater  part  of  the  load  ? 

13.  How  would  you  hitch  three  horses  to  an  evener  so  that  each 
must  pull  the  same  amount  ? 

14.  Why  is  a  greater  pull  required  at  A,  Fig.  31,  than  at  B  to  keep 
the  bar  in  place? 

Problems 

1.  In  a  four-mile  race  between  the  Yale  and  Harvard  crews, 
the  time  of  the  winning  crew  was  21  min.  and  10  sec.     What  was  the 
average  speed  in  miles  per  hour  ?     In  feet  per  second  ? 

2.  At  6  o'clock  on  June  29,  1907,  a  24-hour  run  was  finished 
by  a  six-cylinder  Napier  motor  car,  at  Weybridge,  England.     The 
distance  covered  was  1581  miles  and  1310 'yards.     What  was  the 
speed  in  miles  per  hour  and  in  feet  per  second  ? 

3.  If  the  motor  car  in  problem  2  weighed  3600  Ib.,  how  would  its 
average  momentum  compare  with  that  of  a  freight  car  weighing 
30,000  Ib.  moving  at  the  rate  of  16  mi.  per  hour? 

4.  Suppose  a  body  to  fall  from  a  captive  balloon  and  to  strike 
the  earth  in  5  sec.     Find  its  velocity  on  striking,  the  entire  space 
passed  over,  and  the  space  passed  over  in  the  last  second.     (Take 
g  =  32.16  ft. ;  make  no  allowance  for  the  resistance  of  the  air.) 


68  THE   MECHANICS  OF  SOLIDS 

6.  Suppose  the  body  to  be  thrown  vertically  downward  from  a 
balloon  with  a  velocity  of  40  ft.  per  second,  and  to  strike  the  earth 
in  5  sec.  Find  v,  S,  and  s,  as  before. 

6.  Suppose  a  body  to  be  thrown  horizontally  from  a  captive 
balloon  with  a  velocity  of  80  ft.  per  second  and  to  strike  the  earth 
in  5  sec.     Construct  the  curve  of  the  path  it  will  take. 

7.  A  rifle  was  fired  in  a  horizontal  direction  with  a  velocity 
of  900  ft.  per  second,  from  the  top  of  a  vertical  cliff  100.5  ft.  high, 
standing  on  the  seashore.     How  far  from  the  base  of  the  cliff  did 
the  ball  strike? 

8.  A  baseball  was  thrown  over  a  flagpole  30.63  m.  high,  just 
clearing  it  at  the  very  top  of  its  path.     How  long  after  it  was  thrown 
did  it  strike  the  ground?    What  was  the  vertical  component  of  its 
velocity?     Does  it  make  any  difference  how  far  from  the  pole  the 
ball  is  thrown?    Explain  the  reason  for  your  answer. 

9.  A  rifle  ball  has  a  velocity,  the  horizontal  component  of 
which  is  1028  ft.  per  second  when  it  is  fired  at  such  an  elevation 
that  its  range  is  3084  ft.    What  is  the  greatest  height  the  ball 
reaches? 

10.  The  acceleration  of  a  ball  rolling  down  an  inclined  plane  is 

3  ft.  per  second  per  second.     How  long  must  the  plane  be  if  it  takes 

4  sec.  for  the  ball  to  roll  to  the  bottom?    What  is  its  final  velocity? 

11.  A  stone  dropped  from  a  bridge  strikes  the  water  hi  3.5  seconds. 
How  high  is  the  bridge? 

12.  A  certain  block  of  marble  weighs  6  kg.  at  New  York  on  a 
spring  scale.     To  how  many  dynes  is  this  weight  equal  ? 

13.  Three  ropes  are  fastened  to  a  ring.     A  boy  pulls  on  the  first 
rope  to  the  east  with  a  pull  of  40  lb.,  another  to  the  south  with  a  pull 
of  60  lb.,  and  a  man  pulls  the  third  rope  in  such  a  direction  and 
with  such  a  force  as  to  keep  the  ring  stationary.     How  much  must 
the  man  pull  and  in  what  direction?    Find  the  direction  by  the 
graphical  method. 

14.  A  sailor,  on  a  ship  that  is  sailing  at  the  rate  of  10  mi.. per  hour, 
climbs  from  the  deck  to  a  point  on  the  rigging  50  ft.  above  in  half  a 
minute.     Show  by  a  figure  the  path  he  takes  through  the  air,  and 
compute  its  length. 

15.  A  trolley  car  going  north  at  the  rate  of  16  mi.  per  hour  meets 
an  east  wind  having  a  velocity  of  30  ft.  per  second.     From  what 


MOTION,  VELOCITY,  AND  FORCE 


69 


direction  does  the  wind  seem  to  come,  and  what  velocity  does  it  seem 
to  have? 

16.  A  weight  of  300  Ib.  is  suspended  from  a  pole  resting  on  the 
shoulders  of  two  men.     If  one  man  carries  three  fifths  of  the  load, 
and  is  4  ft.  from  the  weight,  how  far  is  the  other  man  from  it  ? 

17.  Two  parallel  forces,  one  of  36  Ib.  and  one  of  64  Ib.,  act  on  one 
side  of  a  wooden  bar  at  a  distance  of  9  ft.  from  each  other.     Where 
must  a  third  parallel  force  be  applied  to  keep  the  bar  in  equilibrium  ? 
How  great  a  force  must  it  be  and  in  what  direction  must  it  act? 

18.  A  weight  of  32  Ib.  is  suspended 
from  a  hook  at  At  by  a  cord  AB.    A  sec- 
ond cord  is  tied  at  B  and  this  is  pulled 
horizontally  in  the  direction  BC  until  the 
cord  A  B  makes  an  angle  of  30°  with  its 
original  vertical  position.     Find  the  pull 
on   BC  and  the  tension   on  A.    Solve 
graphically.     Suspend  any  weight,  attach 
the  hook  of  a  spring  balance  at  B,  and 
prove  experimentally. 

19.  An  ocean  steamer  is  going  north- 
east   at  the  rate  of  400   mi.    per   day 
(24  hr.).     How  far  north  is  she  going  per 
hour  ?    How  far  east  ? 

20.  A  balloon  rises    with  a  vertical 


FIG.  46 


velocity  of  138  ft.  per  minute,  while  the  wind  causes  it  to  take  a 
path  making  an  angle  of  60°  with  the  ground.  What  is  the  hori- 
zontal velocity  of  the  wind  ?  What  is  the  speed  of  the  balloon  ? 
Solve  graphically. 

21.  Three  boys  carry  a  boat  that  weighs  250  Ib.    The  center 
of  gravity  or  point  of  application  of  the  weight  of  the  boat  is  8  ft. 
from  the  stern.     One  boy  lifts  from  the  stern  and  the  other  two  from 
a  cross  stick  placed  underneath  the  boat.     How  far  from  the  center 
of  gravity  must  the  cross  stick  be  placed  if  each  boy  lifts  the  same 
amount  ?    How  far  must  it  be  if  the  two  boys  carry  three  fourths  of 
the  boat? 

22.  At  New  York  a  ball  weighing  9  Ib.  is  swinging  around  a  circle 
5  ft.  in  diameter  with  a  velocity  of  22  ft.  per  second.     What  pull 
must  be  used  to  keep  the  ball  in  its  path? 


70 


THE  MECHANICS  OF  SOLIDS 


II.    ENERGY  AND  WORK 

70.  Energy.  —  The  head  of  a  pile  driver  (Fig.  47)  falling 
upon  a  pile  forces  the  pile  into  the  ground  to  a  depth  which 

depends  upon  the  weight 
of  the  head  and  the 
height  from  which  it  falls. 
Increase  either,  and  its 
capacity  for  doing  work, 
that  is,  its  energy,  is  in- 
creased, and  the  pile  'is 
driven  farther  into  the 
ground.  If  we  watch  the 
engine  of  a  pile  driver 
while  it  is  pulling  the  iron 
head  to  the  top  of  the 
frame,  we  shall  see  that  it 
is  doing  work.  When  the 
head  has  been  raised  and 
is  held  in  position,  the 
work  of  the  engine  stops, 
but  the  steam  pressure  is 
still  there  ready  to  be 
used  at  short  notice. 
Steam  under  pressure  is  said  to  possess  energy.  Energy 
may  be  defined  as  the  capacity  for  doing  work.  It  is 
measured  by  the  amount  of  work  it  is  capable  of  doing. 

71.  Potential  Energy. — We  have  only  to  loosen  the  catch 
which  holds  the  head  in  place  to  find  that  the  head  also  is 
ready  to  do  work.    When  the  catch  is  loosened,  the  head  falls, 
strikes  upon  the  top  of  the  pile,  and  its  capacity  for  doing 
work  is  shown  by  driving  the  pile  into  the  ground.     If  the 


FIG.  47.  — Pile  Driver 


ENERGY  AND  WORK  71 

head  is  again  raised,  but  only  half  as  high,  it. will  be  found 
on  dropping  it  that  but  half  as  much  work  is  done.  This 
shows  that  the  height  from  which  the  head  falls  must  be 
taken  into  account,  as  well  as  the  weight  of  the  head  itself. 
The  energy  that  a  body  has  on  account  of  its  position  is 
called  potential  energy.  The  work  that  has  been  done  on  a 
body  to  place  it  in  a  certain  position  is  the  measure  of  its 
potential  energy.  This  measure  is  expressed  by  the  equation 

P.E.  =  Wh,  (19) 

in  which  W  is  the  weight  of  the  body  and  h  is  its  vertical 
height  above  the  point  with  reference  to  which  its  potential 
energy  is  measured.  Energy  is  measured  in  the  same  units 
as  work.  For  instance,  the  potential  energy  of  a  10-lb.  weight 
ready  to  fall  6  ft.  is  60  foot  pounds. 

72.  Kinetic  Energy.  —  When  the  head  strikes  the  pile, 
the  work  that  had  been  stored  up  as  potential  energy  in 
raising  the  head  to  its  position  of  rest  becomes  available 
on  account  of  the  velocity  acquired  in  the  fall.  This  form 
of  energy  which  is  dependent  upon  the  velocity  of  a  body  is 
called  kinetic  energy.  The  work  that  has  been  done  on  a 
body  to  give  it  a  certain  velocity  is  a  measure  of  its  kinetic 
energy.  We  have  already  learned  that  work  =  force  X  dis- 
tance, and  that  force  (in  absolute  units)  =  mass  X  accelera- 
tion ;  hence  we  may  write  as  an  expression  of  kinetic  energy, 

K.E.  =  FS  =  MaS. 

But  (Formula  4)  S  =  %at2;  hence  K.E.  =  }  MaW,  and 
since  v  =  at  (Formula  3), 

K.E.  =  J  M&,  (20) 

in  which  v  is  the  velocity  per  second,  and  K.E.  is  expressed 
in  absolute  units. 


72  THE  MECHANICS  OP  SOLIDS 

If  K.E.  is  to  be  expressed  in  gravity  units, 

K.E.  =  FS  =  ^;  whence  K.E.  =  -        .          (21) 
9  20 

Since  g  (at  New  York)  is  32.16  ft.,  the  formula   may  be 
written 


64^' 

when  the  weight  is  given  in  pounds,  the  velocity  per  second 
in  feet,  and  the  result  is  required  in  foot  pounds. 

73.  The    Transformation    of    Energy.  —  The    pendulum 
affords  a  ready  means  of  showing  that  potential  energy  may 

be  changed  into  kinetic,  and  vice 
versa.  Let  a  ball  A  be  suspended 
by  a  cord  from  a  fixed  point  P 
(Fig.  48).  The  ball  when  at  rest 
will  take  the  position  A,  where, 
since  it  is  at  rest  at  its  lowest  point, 
it  has  neither  potential  nor  kinetic 
energy.  In  order  to  move  it  to  B, 
work  must  be  done  on  it  equivalent 

to  raising  it  through  the  vertical  distance  DB.  At  B  it  has 
potential  energy  only,  and  if  it  is  allowed  to  swing,  it  will 
move  down  the  arc,  losing  potential  energy  and  gaining 
kinetic,  until  it  reaches  A,  when  its  energy  will  all  be  kinetic 
and  will  be  sufficient  to  carry  it  up  the  other  branch  of  the 
arc  to  the  point  (7,  a  distance  CE  above  the  horizontal  line, 
practically  equal  to  DB  ;  and  here  its  energy  is  again  all  po- 
tential. If  a  spiral  spring,  the  spring  for  a  screen  door,  for 
example,  is  used  as  the  suspending  cord,  and  a  kilogram 
weight  for  the  pendulum  bob,  a  further  transformation  takes 
place,  the  to-and-fro  vibration  changing  into  a  vertical 
vibration  and  then  back  again  repeatedly. 


ENERGY  AND  WORK  73 

The  kinetic  energy  of  the  pendulum  is  employed  in  raising 
it  against  the  force  of  gravity  and  restoring  its  potential 
energy.  The  case  of  a  rifle  ball  striking  against  a  stone  wall 
is  somewhat  different.  The  motion  of  the  ball  is  stopped 
and  its  kinetic  energy  is  transformed  chiefly  into  mechanical 
work  and  heat,  for  the  ball  itself  is  shattered,  the  wall  is  de- 
faced, .and  if  the  velocity  is  very  great,  heat  enough  is  pro- 
duced to  melt  part  of  the  ball. 

The  potential  energy  stored  in  coal  may  be  transformed 
into  heat  energy  by  combustion,  this  into  kinetic  energy,  if 
applied  to  a  boiler  and  steam  engine,  and  this  into  electrical 
energy,  if  the  engine  is  used  to  turn  a  dynamo. 

74.  The  Conservation  of  Energy.  —  When  a  ball  is  fired 
from  a  rifle,  none  of  the  energy  that  is  developed  by  the 
combustion  of  the  powder  is  lost,  but  it  is  all  transformed 
into  other  forms  of  energy.  Both  the  rifle  and  the  ball  are 
put  in  motion,  producing  kinetic  energy ;  the  air  is  thrown 
into  vibration,  producing  sound ;  the  ether  is  thrown  into 
vibration,  producing  light ;  and  to  these  results  must  be  added 
the  heat  of  the  combustion.  The  sum  of  all  these  forms  of 
energy  is  equal  to  the  potential  energy  of  the  powder,  and 
there  is  no  loss. 

By  extending  the  consideration  to  all  kinds  of  transfor- 
mation of  energy,  scientists  have  reached  the  conclusion 
that  energy  can  neither  be  created  nor  destroyed,  and  hence 
that  the  total  amount  of  energy  in  the  universe  is  constant. 

The  pile  driver  is  a  good  example  of  both  the  transforma- 
tion and  the  conservation  of  energy.  As  the  head  rises  from 
the  top  of  the  pile  the  work  of  the  engine  gives  it  potential 
energy.  The  measure  of  this  is  the  amount  of  work  it  is 
capable  of  doing.  This  is  changed  into  kinetic  energy  as 


74  THE   MECHANICS  OF  SOLIDS 

the  head  falls,  and  when  it  strikes  the  top  of  the  pile  it  delivers 
the  same  amount  of -kinetic  energy  that  it  had  of  potential 
energy  when  it  started.  That  is,  its  kinetic  energy  equals 
its  potential  energy.  A  simple  way  to  compute  kinetic 
energy  is  to  find  how  far  the  velocity  of  the  moving  body 
would  carry  it  vertically  upward  and  use  that  distance  for 
h  in  the  expression  for  potential  energy. 

75.  Work.  —  Whenever  a  force  acts  upon  a  body  in  such 
a  way  as  to  move  it,  or  to  modify  its  motion,  work  is  said 
to  be  done.     However  great  the  force  used,  no  work  is  done 
unless  the  body  is  moved.     A  man  going  upstairs,  a  boy 
playing  ball,  and  a  crane  lifting  loads  from  one  position  to 
another  (Fig.  49),  are  all  doing  work. 

76.  Measurements  of  Work.  —  The  amount  of  work  done 
varies  directly  as  the  force  employed  and  the  distance  through 
which  it  acts.     Hence  the  formula  may  be  written 

Work  =  FS.  (22) 

There  are  four  fundamental  units  of  work,  as  follows,  de- 
pending on  the  units  in  which  F  and  S  are  expressed : 

Absolute  Units 

I.  The  erg  is  the  work  done  by  a  force  of  1  dyne  acting 
through  a  distance  of  1  centimeter. 

II.  The  foot  poundal  is  the  work  done  by  a  force  of  1 
poundal  acting  through  a  distance  of  1  foot. 

Gravity  Units 

III.  The  kilogrammeter  is  the  work  done  in  raising   1 
kilogram  1  meter  vertically  against  the  force  of  gravity. 

IV.  The  foot  pound  is  the  work  done  in  raising  1  pound 
1  foot  vertically  against  the  force  of  gravity. 


ENERGY  AND   WORK 


75 


FIG.  49.  —  Loading  of  a  Railroad  Car  on  a  Ship 

This  picture,  made  in  Seattle,  shows  a  railroad  car  being  put  on  board  for  shipment 
to  Alaska.  By  means  of  the  crane  it  was  lifted  off  its  tracks,  at  the  left,  and  is  now 
being  swung  into  position  over  the  ship. 


76  THE  MECHANICS  OF  SOLIDS 

Other  units  of  work  may  be  used,  depending  upon  the 
conditions.  Since  the  erg  is  a  very  small  unit,  a  larger  unit, 
called  the  joule,  is  sometimes  used ;  1  joule  =  107  ergs,  or 
10,000,000  ergs.  The  foot  pound  and  the  kilogrammeter 
are  the  units  generally  used  in  engineering  work. 

TABLE  OF  EQUIVALENTS  AT  NEW  YORK 

1  pound  =  32.16  poundals. 

1  foot  pound  =  32.16  foot  poundals. 

1  poundal  -=  -^-^  pound  =  £  oz.  nearly. 

o^.lO 

1  gram  =  980.2  dynes. 

1  kilogrammeter  =  98,020,000  ergs. 

1  kilogrammeter  =  7.233  foot  pounds. 

Formula  22  shows  that  if  a  man  lifts  a  stone  weighing 
100  Ib.  2\  ft.  high,  the  work  done  is  100  X  2|  =  250  foot 
pounds,  and  that  if  an  engine  raises  12  kg.  20  m.  high,  the 
work  done  is  12  X  20  =  240  kilogrammeters. 

77.  Time  is  not  an  Element  in  Work.  —  Too  great  stress 
cannot  be  put  upon  the  statement  that  the  time  employed 
in  doing  a  certain  amount  of  work  has  nothing  whatever 
to  do  with  the  amount  of  work  done.     When  1  Ib.  is  raised 
1  ft.,  exactly  1  foot  pound  of  work  is  done,  no  matter  whether 
the  time  taken  in  the  raising  is  1  second  or  1  hour  or  40  hours. 
The  dealer  who  pays  a  lump  sum  for  the  unloading  of  a  boat- 
load of  coal,  pays  for  that  alone,  and  not  for  the  time  that  may 
be  consumed  by  the  use  of  an  imperfect  hoisting  machine. 

78.  Time ;  Rate  of  Work ;  Horse  Power.  —  The  work  done 
in  a  given  time,  divided  by  the  time,  gives  the  average  rate 
of  doing  work,  or  power. 

The  C.  G.  S.  unit  of  power  is  the  erg  per  second.  In  prac- 
tical work  the  joule  per  second  is  used;  this  is  called  the 


ENERGY  AND  WORK  77 

watt  in  honor  of  James  Watt,  the  inventor  of  the  steam 
engine. 

1  watt  =  1  joule  per  second  =  107  ergs  per  second. 
1  kilowatt  =  1000  watts 

In  the  F.  P.  S.  system  the  unit  of  power  is  the  foot  poundal 
per  second.  This  is  a  small  unit  and  is  seldom  used,  the 
practical  unit  being  the  horse  power,  which  means  a  rate  of 
33,000  foot  pounds  per  minute,  or  550  foot  pounds  per 
second ; 1  hence  the  expression  for  horse  power  is 

No  H  P  -        No-  foot  pounds  (23) 

"  33000  X  No.  minutes 

This  unit  was  introduced  by  James  Watt  and  its  value  was 
assigned  by  him.  It  is  the  work  that  would  be  done  in  one 
minute  by  a  horse  walking  at  the  rate  of  three  miles  per 
hour  and  raising  a  weight  of  125  pounds  at  the  same  rate  by 
a  rope  passing  over  a  pulley.  One  horse  power  is  rated  at 
746  watts  or  0.746  kilowatts.  Hence  the  horse  power  is  prac- 
tically three  fourths  of  a  kilowatt  and  one  kilowatt  equals 
one  and  one  third  horse  power. 

The  kilowatt  is  used  to  measure  the  power  output  of 
electric  generators,  while  the  steam  power  input,  used  in 
engines  or  turbines,  is  measured  in  horse  power  or  myria- 
watts  (1  myriawatt  =  10  kilowatts). 

1  The  relation  between  the  horse  power  and  the  watt  is  deter- 
mined as  follows : 

1  horse  power  =  550  foot  pounds  per  second. 

1  foot  =  30.48  centimeters. 

1  pound  =  453.6  grams. 

1  gram  =981  dynes.      (The  number  varies  with  the  value 

of  g ;  this  is  about  the  value  for  the  latitude 
of  Paris.) 

Hence  1  horse  power  =  550  X  30.48  x  453.6  x  981  =  7,459,671,542 
ergs  per  second.  Hence  1  horse  power  =  745.97  watts. 

In  New  York,  g =980.2  dynes,  hence  one  horse  power  =  745. 36  watts. 


78  THE  MECHANICS  OP  SOLIDS 


Questions 

1.  Define  work;    energy;    horse  power;    kilowatt.     Illustrate 
each. 

2.  State  the  difference  between  potential  and  kinetic  energy. 

3.  What  is  meant  by  conservation  of  energy  ?     Transformation 
of  energy?     Give  examples  of  the  latter. 

4.  Can  force  be  used  without  doing  work  ?     Give  examples. 

6.  What  element  enters  into  rate  of  work  or  power,  that  does 
not  enter  into  work  ? 

6.  A  boy  tosses  a  2-lb.  weight  vertically  upward  with  such  a 
velocity  that  it  rises  for  two  seconds.    What  is  its  greatest  kinetic 
energy?     What  is  its  greatest  potential  energy? 

7.  A  4-lb.  weight  was  allowed  to  drop  freely  for  4  seconds. 
From  what  height  did  it  fall?     What  energy  did  it  acquire? 

8.  What  is  the  kinetic  energy  of  a  5-lb.  mass  having  a  veloc- 
ity of  96  ft.  per  second? 

9.  How  much  work  is  done  if  a  kilogram  force  acts  upon  a -body 
and  moves  it  1500  cm.  ? 

10.  A  2-lb.  ball  falls  for  2  sec.  and  rebounds  a  distance  of  40  ft. 
How  much  mechanical  energy  has  the  ball  lost  ?     What  has  become 
of  the  lost  energy  ? 

11.  A  boy  holds  a  2-lb.  stone  in  his  hand.     Is  he  doing  any 
work  ?    Does  he  do*  any  work  when  he  throws  the  stone  ?    What 
kind  of  energy  does  he  give  to  the  stone  ? 

12.  A  horse  pulling  a  load  uphill  gives  out' when  halfway  up  and 
is  only  able  to  keep  the  load  from  sliding  back.      Is  he  doing  any 
work?    Why? 

13.  If  he  were  unable  to  keep  the  load  from  sliding  back,  would 
any  work  be  done  ?     If  so,  by  what  force  ? 

14.  What  transformations  of  energy  take  place  in  the  working  of 
a  locomotive? 

Problems 

1.  How  much  work  is  done  in  drawing  a  sled  300  ft.  if  the  force 
required  is  24  lb.? 

2.  How  much  work  is  done  in  carrying  a  ton  of  coal  (2240  lb.) 
up  two  flights  of  stairs,  the  total  height  being  21  ft.? 


ENERGY   AND   WORK  79 

3.  On  attaching  a  spring  scale  to  a  block  of  wood  and  pulling 
it  over  a  floor,  the  reading  of  the  scale  was  found  to  be  16  kg.   How 
much  work  was  done  in  drawing  the  block  over  a  distance  of  22  m.? 

4.  A  boy  with  his  toboggan  weighs  140  Ib.     He  slides  down  a 
chute  150  ft.  long  in  2.5  seconds  and  has  a  velocity  of  40  ft.  per 
second  at  the  bottom.     What  is  his  acceleration,  and  what  kinetic 
energy  does  he  have  at  the  end  of  his  trip? 

6.^  How  much  work  does  a  boy  weighing  120  Ib.  do  in  walking 
upstairs  to  a  height  of  12  ft.? 

6.  A  man  weighing  186  Ib.  carries  a  package  weighing  32  Ib. 
upstairs  from  the  first  to  the  third  floor  of  a  building.     How  much 
work  does  he  do  if  the  vertical  distance  is  19  ft.?     How  much  does 
he  do  upon  himself?     How  much  in  carrying  the  package? 

7.  What  horse  power  is  required  to  raise  3.5  long  tons  (a  long  ton 
is  2240  Ib.)  from  a  mine  780  ft.  deep  in  1.5  minutes?    What  is. the 
power  of  the  engine  in  watts? 

8.  What  is  the  potential  energy  of  the  head  of  a  pile  driver 
weighing  500  Ib.  when  it  is  28  ft.  above  the  end  of  the  pile?     When 
it  is  16  ft.  above  the  end  of  the  pile?     If  it  is  let  fall  from  the  height 
of  28  ft.,  it  will  strike  the  pile  with  a  velocity  of  42.438  ft.  per  second. 
What  will  be  its  kinetic  energy  on  striking? 

9.  A  quarry  crane  hoists  a  block  of  marble  6  ft.  long,  4  ft.  wide, 
and  2.5  ft.  thick.     How  much  work  is  done  in  raising  the  block 
12  ft.  if  the  marble  weighs  160  Ib.  per  cubic  foot?     Neglecting  fric- 
tion, what  must  be  the  horse  power  of  the  motor  to  do  this  in  3  min.? 
What  is  the  potential  energy  of  the  block  at  that  height? 

10.  How  long  will  it  take  a  66-horse  power  engine  to  raise  a  weight 
of  299,000  Ib.  to  a  height  of  300  ft.? 

11.  How  many  horse  power  must  be  developed  by  a  locomotive 
when  pulling  a  train  lOmi.per  hour,  the  force  required  being  12,000 Ib.? 

12.  An  elevator  weighing  1800  Ib.  more  than  its  counterweight 
carries  a  load  of  6  people  of  an  average  weight  of  140  Ib.  each. 
Neglecting  friction,  what  must  be  the  horse  power  of  a  motor  that 
will  lift  it  72  ft.  in  30  sec.? 

13.  An  ordinary  brick  weighs  5  Ib.     How  long  would  it  take  to 
fall  to  the  ground  from  the  top  of  the  Kodak  Company's  chimney  in 
Rochester,  which  is  366  ft.  high?     With  what  velocity  would  it 
strike?    What  would  be  its  kinetic  energy  on  striking? 


80  THE  MECHANICS  OF  SOLIDS 

III.     GRAVITATION  AND  GRAVITY 

79.  Law  of  Universal  Gravitation.  —  Gravitation  is  the 
name   given   to   the   mutual   attraction    between   different 
bodies  of  matter.     The  matter  considered  may  be  two  books 
lying  on  a  table,  or  two  stars  separated  by  millions  of  miles. 
The  attraction  is  universal,  and  the  Law  of  Universal  Gravita- 
tion may  be  stated  as  follows : 

Every  particle  of  matter  in  the  universe  attracts  every  other 
particle  with  a  force  that  varies  directly  as  the  product  of  the 
masses  of  the  particles  and  inversely  as  the  square  of  the  dis- 
tance between  them.  This  leads  to  the  formula  which  is  appli- 
cable to  all  mutual  attractions,  namely, 

(24) 

in  which  a  is  the  unit  of  attraction ;  i.e.,  the  attraction  be- 
tween two  units  of  mass  at  a  unit's  distance. 

For  comparing  two  attractions  of  the  same  kind  we  may 
write  the  proportion 

„        ,    _  Mm  m  M'm! 
*o  •*  0-    -#-:(df)T' 

The  momenta  given  by  mutual  attraction  to  the  two  bodies 
between  which  the  attraction  acts,  are  equal.  A  man  stand- 
ing in  a  rowboat  and  pulling  on  a  rope  that  is  fast  to  a  sloop 
moves  the  boat  faster  than  the  sloop,  but  only  because  its 
mass  is  much  less.  The  momentum  imparted  to  the  sloop 
is  equal  to  that  given  to  the  rowboat. 

80.  Gravity.  —  While  the  term  gravitation  is  applied  to 
the  universal  attraction  existing  between  particles  of  matter, 
the  more  restricted  term  gravity  is  applied  to  the  attraction 
that  exists  between  the  earth  and  bodies  upon  or  near  its 


GRAVITATION  AND  GRAVITY  81 

surface.  The  law  given  above  applies  to  gravity,  provided 
that  d  is  measured  in  a  straight  line  from  the  center  of  the 
earth  to  the  center  of  mass  of  the  body.  This 
line  is  called  a  vertical  line,  or  sometimes  a  phimb 
line  (from  the  Latin  word  plumbum,  which  means 
"  lead  "),  as  vertical  lines  are  frequently  deter- 
mined by  suspending  a  mass  of  lead,  the  plumb 
bob,  at  the  end  of  a  cord  (Fig.  50). 

81.  Weight. — The  weight  of  a  body  is  the  meas- 
ure of  the  mutual  attraction  that  exists  between  the 
earth   and  that  body.     This  force  is  the  resultant 
of  the  attractions  between  the  earth  and  all  the 
particles  of  the  body. 

The  weights  of  any  two  bodies  at  the  same  place 
are  proportional  to  their  respective  masses. 

Since  the  polar  diameter  of  the  earth  is  26^  miles 
less  than  the  equatorial,  it  is  evident  that  the 
weight  of  a  body  will  vary  with  the  latitude  as  well  as 
with  the  elevation  above  the  sea  level.  The  weight  of  a 
body  carried  from  either  pole  toward  the  equator  is  decreased 
by  the  increase  in  its  distance  from  the  center.  There  is 
also  an  apparent  decrease,  owing  to  the  increase  in  the  cen- 
trifugal force  of  the  earth's  rotation.  Bodies  on  the  equator 
move  with  a  velocity  of  more  than  a  thousand  miles  per 
hour,  and  the  centrifugal  force  there  is  •$%$  of  the  force  of 
gravity,  while  at  the  poles  it  is  zero.  Should  the  earth 
rotate  17  times  as  fast  as  it  now  does,  the  centrifugal 
force  would  equal  the  force  of  gravity,  since  centrifugal 
force  varies  as  the  square  of  the  velocity  (Formula  17). 

82.  Weight  above  the  Surface.  —  The  maximum  weight 
of  a  body  is  at  the  surface  of  the  earth.     If  a  body  is  removed 

Rev. 


82 


THE   MECHANICS   OF  SOLIDS 


above  the  sea  level,  as  on  the  top  of  a  mountain,  or  in  a 
balloon,  the  distance  d  between  it  and  the  center  of  the  earth 
is  increased,  and  its  weight  is  diminished.  The  relation  be- 
tween weight  at  the  surface  and  weight  above  the  surface 
may  be  expressed  by  the  proportion 

W:w  =  d*:D\  (25) 

in  which  W  is  the  weight  at  the  surface ;  w,  the  weight  above 
the  surface ;  D,  the  distance  from  the  center  to  the  surface 
of  the  earth ;  and  d,  the  distance  of  the  body  from  the  earth's 
center. 

83.  Center  of  Gravityv — The  attraction  of  gravity  on 
any  body  tends  to  draw  its  particles  toward  one  point,  and 
hence,  strictly  speaking,  the  directions  of  these  forces  are  not 
parallel.  As  the  radius  of  the  earth  is  very  large,  however, 
compared  with  the  size  of  any  object  which  is  weighed,  their 
divergence  from  parallel  lines  is,  practically,  not  measurable. 

The  point  of  application  of 
the  resultant  of  all  the  par- 
allel forces  (§  62)  that  make 
up  the  weight  of  a  body  is 
its  center  of  gravity,  center  of 
mass,  or  center  of  inertia. 

Demonstration.  —  Fit  in  a 
small  wooden  handle  (or  in  a 
fixed  support),  two  wires  (Fig. 
51) :  one,  A,  straight  and  the 
other,  B,  bent  twice  at  right 
angles.  In  a  piece  of  thin 
board  C  of  any  shape  bore  holes 
D  and  E  in  two  corners.  Suspend  the  board  by  one  of  these  holes 
D  from  the  wire  B,  and  from  A  suspend  a  plumb  line.  See  that  D 
is  exactly  halved  by  the  plumb  line  when  at  rest,  and  mark  a 


FIG.  51 


GRAVITATION  AND   GRAVITY  83 

point  F  opposite  the  line.  Suspend  the  board  from  the  hole  E,  and 
mark  the  point  G.  Draw  lines  DF  and  EG,  and  their  intersection 
0  will  determine  the  center  of  gravity.  Test  the  accuracy  of  the 
worlx,  by  making  a  hole  at  0  and  rotating  on  the  end  of  A. 

Find,  in  the  same  way,  the  centers  of  gravity  of  a  triangle, 
a  square,  a  rectangle,  and  a  circle. 

In  the  above  cases  the  center  of  gravity  is  midway  be- 
tween the  two  surfaces  at  the  point  0.  It  would  still  be 
at  0,  if  the  thickness  of  the  board  were  infinitely  reduced ; 
hence  we  may  speak  of  the  center  of  gravity  of  a  surface. 
The  center  of  gravity  of  any  body  may  be  found  by  sus- 
pending it  successively  from  two  points  on  the  body  and 
finding  the  intersection  of  the  lines  of  direction  from  those 
points  of  support  to  the  center  of  the  earth.  This  is  be- 
cause a  body  suspended  from  any  point  will  hang  with  its 
center  of  gravity  vertically  below  the  point  of  suspension. 
The  center  of  gravity  is  frequently  outside  the  substance 
of  the  body,  as  in  the  case  of  a  ring. 

84.  The  Center  of  Gravity  of  a  Number  of  Bodies  rigidly 
connected  may  be  determined  by  considering  the  weight 
of  each  body  as  a  parallel  force  ap- 
plied  at  its  center  of  gravity,  and 
then  finding  the  point  of  applica- 
tion of  the  resultant  of  these  forces 
(§  62).  Suppose  three  parallel 
forces,  P,  Q,  and  S,  to  be  applied 
at  three  points,  A,  B,  and  C, 
rigidly  connected,  as  in  Fig.  52.  FlG-  52 

The  resultant  Rf  of  P  and  Q  will  equal  P  +  Q,  and  its 
point  of  application  will  be  at  a  point  D,  determined  by  the 
proportion  (§  62) 

P:R'=  DB-.AB, 


84 


THE   MECHANICS  OF  SOLIDS 


whence 


z>sy^- 


X 


e 


Now  connect  D  with  C,  and  three  forces  P,  Q,  and  S  are 
replaced  by  the  two  forces  S  and  R' '.  Find  in  the  same  way 
the  point  of  application  E  of  their  resultant,  and  this  will 
be  the  center  of  gravity  of  the  system. 

Demonstration.  —  Select  a  board  of  uniform  thickness  and  put 
in  it  a  screw  hook  close  to  each  corner.     Weigh  the  board,  and 

determine  its  center  of  gravity  by 
calculation.  Suspend  from  each 
hook  a  known  weight,  as  2,  4, 
and  6  pounds,  for  example.  -Let 
each  member  of  the  class  make  a 
drawing  of  the  board  and  locate 
on  it  the  position  of  the  center  of 
gravity  of  the  board  and  the  po- 
sition of  each  weight,  and  deter- 
mine the  center  of  gravity  of  the 
system  by  construction.  When 
this  has  been  done,  put  a  screw 
eye  in  the  upper  side  of  the  board  at  the  point  found,  and  lift  the 
board  and  weights  with  a  spring  scale.  Does  the  board  hang 
horizontally?  What  is  the  weight  of  the  system? 


FIG.  53 


FIG.  54 


85.  Equilibrium.  —  Pierce  a  disk  of  cardboard  with  two 
holes,  one  at  the  center,  and  the  other  near  the  edge.  Sus- 
pend it  on  a  pin  P  (Fig.  54),  from  the  hole  near  the  edge 


GRAVITATION  AND  GRAVITY 


85 


and  it  will  take  the  position  a,  such  that  the  center  will  lie 
in  the  vertical  line  below  P.  If  the  disk  is  moved,  the 
center  of  gravity  will  be  raised,  and  the  disk  will  tend  to 
return  to  its  first  position.  This  condition  is  that  of  stable 
equilibrium. 

If  the  disk  is  placed  in  position  b,  and  a  slight  push  is 
given  to  it,  the  center  of  gravity  will  be  lowered;  and  the  disk 
will  tend  to  go  farther  from  its  position.  This  is  the  condi- 
tion of  unstable  equilibrium. 

Place  the  disk  in  position  c.  Set  it  in  motion,  and  the 
center  of  gravity  neither  rises  nor  falls,  and  the  disk  comes  to 
rest  in  one  position  as  well  as  another.  This  is  the  condition 
of  neutral  equilibrium. 

86.  Stability.  —  When  a  body  is  in  a  condition  of  stable 
equilibrium,  (a)  a  vertical  line  from  the  center  of  gravity  will 
either  pass  through  the  point 
of  suspension,  or  fall  within 
the  base  of  support ;  and  in 
order  that  a  body  may  have 
great  stability  (b)  the  base 
must  be  large  and  (c)  the 
center  of  gravity  low.  An 
ordinary  pyramid  fulfills 
these  conditions.  The  cen- 
ter of  gravity  of  a  pyramid 
(Fig.  55,  for  example)  is  a  A 
point  (C)  on  a  line  (GF)  join- 
ing the  vertex  and  the  center  of  gravity  of  the  base,  and  at 
a  distance  from  the  base  equal  to  one  fourth  the  length  of 
the  line  (that  is,  CF  =  \GF). 

The  stability  of  an  automobile  is  increased  by  having  the 


FIG.  55 


86 


THE  MECHANICS  OF  SOLIDS 


frame  of  the  "  underslung  "  type  (Fig.  56),  thus  bringing  the 
center  of  gravity  near  the  ground. 


FIG.  56.  —  Underslung  Automobile  Chassis 

87.  Work  Done  in  Overturning  a  Body.  -  -  The  work  that 
must  be  done  to  overturn  a  body  is  a  measure  of  its  stability. 
When  a  cylinder  lies  upon  its  side,  the  only  work  necessary 
to  overturn  it  is  to  overcome  the  friction  between  it  and  the 
surface  upon  which  it  lies,  since  the  center  of  gravity  moves 
in  a  horizontal  line.  If,  however,  the  body  is  a  cube,  the 
center  of  gravity  is  raised  a  distance  ab  every  time  it  is  turned 
over,  and  the  work  done  is  just  the  same  as  would  be  done 
in  lifting  the  cube  through  the  height  ab  (Fig.  57). 


FIG.  57 


A  brick  lying  on  a  table  upon  its  side  has  greater  stability 
than  one  standing  on  end.  The  work  necessary  to  overturn 
it  in  each  case  is  expressed  by  the  formula  Work  =  W  X  ab. 


GRAVITATION  AND  GRAVITY 


87 


In  both  cases  shown  in  Fig.  58  the  highest  position  of  the 
center  of  gravity  is  the  same,  but  the  original  heights  above 


b      i 
a     / 


FIG.  59 


FIG.  58 

the  table  are  unequal  and  so  the  product  W  X  ab  is  greater 
in  A  than  in  B. 

Demonstration.  —  Get  a  brass  ball  such  as  is  used  on  the  ends 
of  curtain  poles.  Remove  the  screw,  enlarge  the  hole,  and  pour 
in  a  little  melted  lead.  When  the 
lead  has  cooled  in  position  A,  put 
the  ball  in  any  other  position,  as 
B,  and  since  a  vertical  line  from 
the  center  of  gravity  C  does  not 
fall  within  the  base  D,  the  ball 
will  roll  and  the  center  of  gravity 
will  fall  until  it  reaches  the  lowest 

possible  position,  when  a  vertical  line  from  C  will  fall  within  the 
base  of  support,  and  the  ball  will  be  in  a  condition  of  stable 

equilibrium. 

The  principle  of  this 
demonstration  is  applied 
in  making  one  kind  of  oil 
cans.  The  ordinary  form 
is  conical  (Fig.  60,  A), 
and'  if  it  is  overturned, 

the    oil    escapes.      But    when    the   base   is   made    in   the 
form  of  a  hemisphere  and  loaded  with  a  little  lead  in  the 


FIG.  60 


88 


THE   MECHANICS  OF  SOLIDS 


bottom  (a),  the  can  will  always  right  itself  and  the  oil  will 
be  retained. 

Questions  . 

1.  Which  is  greater,  the  attraction  of  the  earth  for  a  pound  of 
iron,  or  the  attraction  of  the  pound  of  iron  for  the  earth  ? 

2.  What  effect  will  it  have  upon  the  attraction  between  two 
bodies  to  increase  the  distance  between  them  from  3  ft.  to  6  ft.? 
To  diminish  it  from  3  ft.  to  1  ft.  ? 

3.  The  distance  of  the  sea  level  from  the  center  of  the  earth 
decreases  from  the  equator  to  the  poles.     What  effect  will  this  have 
upon  the  weight  of  a  body  taken  from  the  equator  toward  either 
pole? 

4.  What  effect  will  it  have  upon  the  mass  of  the  body  ? 

6.  Where  is  the  center  of  gravity  of  a  baseball?     Of  a  football? 
Of  a  tennis  racket? 

6.  If  you  take  a  hammer  by  the  handle  and  throw  it  into  the  air 
with  a  twisting  motion,  which  will  describe  the  larger  circle,  the 
handle  or  the  head?     Why? 

7.  In  what  position  will  a  stick  loaded  at  one  end  float  in  water? 
Why? 

8.  Which  is  the  most  stable  body,  a  table  with  a  marble  top  or 

one  with  a  wooden  top,  other  things 
being  equal?     Why? 

9.  A  wooden  rod  R  to  which 
there  is  attached  a  wire  bent  into 
the  form  of  a  semicircle,  and  having 
a  weight  W  attached  at  the  other 
end,  will,  when  supported  on  the  end 
B,  swing  back  and  forth.  Why? 

10.  A  man  standing  with  his  back 
against  a  vertical  wall  cannot  pick 
up  anything  from  the  floor  in  front 
of  him  without  falling.     Why? 
11.  Describe  and  explain  the  difference  between  the  position  of 

a  man  carrying  a  pail  of  water  in  one  hand  and  a  man  carrying  a 

pail  of  water  in  each  hand. 


FIG.  61 


THE    PENDULUM  89 

Problems 

1.  Suppose  three  balls,  weighing  respectively  6,  10,  and  18  lb.,  to 
be  placed  at  the  distances  represented  in  Fig.  62.     If  the  attraction 
(Fg  on  page  SO)  between 

A  and  B  is  9,  \  'hat  will  the  6  jbs. 

attraction  (F'G)  be  between 
A  and  (7?  Bet  ween  B  and  C? 

2.  'The  weight  of  a  body 
at  the  surface  of  the  earth 
is  125  lb.    What  would  be 

its  weight  if  it  were  1000      w  15ft 

mi.  above  the  earth's  sur-     10  lbs-  18  lbs- 

face?    (Take  8000  miles  as  FIG.  62 

diameter  of  earth.) 

3.  Two  iron  balls,  weighing  10  and  6  lb.  respectively,  are  fastened 
to  the  ends  of  a  rod,  with  a  distance  of  4  ft.  between  their  centers. 
Assuming  the  rod  to  be  without  weight,  where  is  the  center  of  gravity 
of  the  system?     Where  is  it  if  the  connecting  rod  weighs  4  lb.? 

4.  A  plank  12  ft.  long,  weighing  60  lb.  is  used  by  two  boys  for 
a  seesaw.     The  boys  weigh  80  lb.  and  120  lb.  respectively.     Where  is 
the  center  of  gravity  of  the  system  if  the  boys  sit  at  the  very  ends  of 
the  plank? 

5.  A  beam  10  ft.  long  and  weighing  300  lb.  has  a  200-lb.  stone 
placed  on  one  end.     The  beam  with  its  load  is  then  balanced  on 
a  log.     How  far  from  the  stone  must  the  log  be  placed? 

6.  A  meter-stick  weighing  100  g.  has  a  kilogram  weight  sus- 
pended from  one  end.     Find  the  center  of  gravity  of  the  system. 

7.  A  flagpole  100  ft.  long  is  to  be  raised.     It  weighs  5  short  tons 
and  the  center  of  gravity  is  30  ft.  from  the  base.     How  many  foot 
pounds  of  work  are  required  to  raise  it? 

8.  How  much  work  is  required  to  turn  over  a  marble  cube  4  ft. 
on  the  edge  if  the  marble  weighs  160  lb.  per  cu.  ft.? 

IV.     THE  PENDULUM 

88.  Simple  Pendulum. — The  ideal  simple  pendulum  is 
one  in  which  a  heavy  material  particle  is  hung  from  a  fixed 
point  with  a  weightless  cord.  It  is  impossible  to  make  such 


90 


THE   MECHANICS  OF  SOLIDS 


a  pendulum,  but  we  get  nearly  the  required  conditions  by 
suspending  a  small  ball  by  a  light  thread. 


89.  Motion  of  a  Pendulum.  —  Whenever  a  pendulum,  as 
OA  (Fig.  63) ,  is  moved  out  of  its  position  of  rest  to  any  other 
position,  as  OB,  it  will,  on  being  re- 
leased, go  back  to  A  and,  owing  to 
the  kinetic  energy  developed  by  its 
fall,  go  on  to  the  position  C,  AC 
being  slightly  less  than  AB.  A  to- 
and-fro  movement  once  over  its  path 
and  back  is  called  an  oscillation,  or 
vibration;  and  the  distance  that  A 
moves  from  its  position  of  rest — AB 
or  AC  •  —  is  the  amplitude  of  the 
oscillation.  In  order  to  find  the 
force  that  causes  the  pendulum  to 
move  over  this  path,  we  must  find 
two  components  of  the  force  of  gravity  BD,  one,  BE,  which 
produces  a  pressure  on  the  point  of  suspension  0,  without 
producing  any  motion,  and  the  other,  BF,  which  acts  at  a 
right  angle  to  BE  and  is  the  force  required.  The  magni- 
tude of  this  force  is  that  fraction  of  the  weight  of  the  pen- 
BF  i 


FIG.  63 


dulum  represented  by 


BD 


This  force   varies  from  zero 


at  A  to  the  weight  of  the  pendulum  at  a  point  on  a  level 
with  0.  Since  in  ordinary  pendulums  the  amplitude  is 
never  large,  the  moving  force  is  always  a  small  part  of  this 
weight. 


1  The  value  of  the  fraction  can  be  obtained  graphically  by  measur- 
ing BF  to  the  same  scale  as  BD. 


THE  PENDULUM 


91 


90.  Laws  of  the  Pendulum.  —  Demonstration.  —  Suspend 
side  by  side  four  pendulums  made  by  fastening  lead  balls  to  the 

ends  of  strong  threads  (Fig. 
64).  Make  two  of  them  1  m. 
long,  one  50  cm.,  and  one  25 
cm.  Measure  the  distance 
from  the  point  of  suspension 
to  the  middle  of  each  ball. 
Vibrate  pendulums  A  and  B. 
Do  two  pendulums  of  the 
same  length  vibrate  in  the 
same  time?  Vibrate  A  and 
B  so  that  one  swings  about 
twice  as  far  as  the  other.  Do 
they  still  vibrate  in  the  same 
time?  Vibrate  B  (or  A}  and 
C.  Does  a  pendulum  half  as 
long  as  another  vibrate  in 
half  the  time?  Vibrate  B  (or  A)  and  D.  What  is  the  relation 
between  the  time  of  vibration  of  one  pendulum  and  that  of  another 
one  fourth  its  length? 

From  an  extension  of  the  above  experiment  it  is  found 
that  the  relation  between  the  time  of  vibration,  or  period, 
of  a  pendulum  and  its  length  may  be  expressed  by  the  formula 


(26) 


9 


in  which  t  is  the  time,  in  seconds,  of  one  complete  vibration, 
and  I  is  the  length  of  the  pendulum.1  In  a  pendulum  of  this 
type  the  length  is  from  the  point  of  support  to  the  middle 
of  the  ball. 


1  The  character  IT  (called  pi}  represents  the  ratio  of  the  circum- 
ference to  the  diameter  of  a  circle,  or  nearly  3.1416;  and  g  repre- 
sents the  acceleration  per  second  per  second  due  to  gravity. 


92  THE   MECHANICS  OF  SOLIDS 

Another  pendulum  ofjength  I'  will  vibrate  in  the  same  place 


fl' 

=  2  TT  \  -, 


in  the  time  t'  =  2  TT  \  -,  and  hence  we  get  the  proportion 

g 

t:t'  =  VJT:  VF.  (27) 

The  times  of  vibration  of  two  pendulums  are  proportional 
to  the  square  roots  of  their  respective  lengths,  and  are  inde- 
pendent of  their  weights  and  of  their  amplitudes  of  vibration. 

91.  The  Seconds  Pendulum.  —  The  vibration,  which  has 
been  defined  as  the  to-and-ho  movement  of  a  pendulum  over 
its  path,  is  called  a  complete  vibration  in  order  to  distinguish 
it  from  the  to-or-fro  movement,  which  may  be  called  a  half 
vibration.  If  t  were  taken  as  the  time  of  a  half  vibration, 

the  formula  would  become  t  =  TT\-.     When   the  time  of 

g 

a  half  vibration  is  one  second,  the  pendulum  is  called  a 
seconds  pendulum;  and  by  solving  the  equation  we  find  its 

length  to  be  /  =  -£-  . 

7T2 

The  value  of  g  at  Philadelphia  is  980.18  cm.  Hence  the 
length  of  the  seconds  pendulum  there  is 

980.18 


92.  The  Compound  Pendulum.  —  Any  body  suspended 
so  as  to  vibrate  in  a  vertical  plane  under  the  influence  of 
gravity  alone  is  a  compound  pendulum.  The  form  generally 
used  for  practical  purposes  is  that  of  a  metallic  bob  sus- 
pended by  a  thin  wire.  The  bob  is  made  lens-shaped,  or 
thin  on  the  edges,  to  offer  less  resistance  to  the  air,  and  is 
arranged  so  that  it  can  be  raised  or  lowered  on  the  wire 
to  regulate  the  length  of  the  pendulum. 


THE   PENDULUM 


93 


FIG.  65 


93.  Length  of  the  Compound  Pendulum. —  Demonstration.— 
From  a  suitable  support  (Fig.  65)  suspend  five  pendulums,  A,  B, 
and  C  being  of  wood,  and 
shaped  as  in  the  figure. 
Vibrate  them  in  pairs. 
Do  they  vibrate  in  the 
same  time  ?  They  are  all 
of  the  same  length  as 
sticks;  are  they  of  the 
same  length  as  pendu- 
lums? Vibrate  each  one 
with  D,  changing  the 
length  of  the  latter  until 
they  vibrate  in  the  same 
time.  Which  is  the  short- 
est as  a  pendulum  ?  Which 
is  the  longest?  Now 
take  the  end  of  the  pendulum  E,  —  which  is  made  by  cutting 
gashes  in  shot  and  pinching  them  upon  a  thread,  —  draw  it  aside 

and  let  it  swing.  Do  the  shot  form 
a  straight  line  or  a  curve?  Why? 

94.  Axis  of  Supension;  Centers 
of  Oscillation  and  Percussion.— 

Demonstration.  —  Bore  a  quarter-inch 
hole  through  the  handle  of  a  baseball 
bat  near  the  end.  Drive  in  a  piece  of 
dowel  pin  for  an  axis,  and  suspend  it  as 
in  A  (Fig.  66).  Set  it  vibrating,  and 
determine  its  length  as  a  pendulum 
by  comparison  with  the  simple  pen- 
dulum D.  Mark  off  this  length  BC 
from  the  lower  side  of  the  pin  B,  and 
put  a  second  pin  through,  with  its 
upper  side  at  C.  Invert  the  bat  and 

vibrate  from  C,  and  it  will  be  found  to  vibrate  in  the  same  time 

as  before. 


FIG,  66 


94  THE    MECHANICS  OF  SOLIDS 

The  axis  at  B,  in  the  left  half  of  Fig.  66,  is  the  axis  of  sus- 
pension. The  point  C  is  the  center  of  oscillation,  and  the 
demonstration  shows  the  important  fact  that  the  axis  of  sus- 
pension and  center  of  oscillation  are  interchangeable. 

The  point  C  is  also  the  center  of  percussion,  and  a  ball 
striking  the  bat  at  this  point  will  receive  the  full  effect  of 
the  blow.  The  position  of  the  hands  in  holding  the  bat 
and  the  swing  given  to  it  will  change  the  position  of  the  center 
of  percussion  slightly.  If  the  ball  is  struck  too  far  from  this 
point,  the  effect  will  be  to  sting  the  hands. 

95.  The  Determination  of  g.  —  By  making  the  axes  of  a 
pendulum  similar  to  the  one  described  in  the  preceding 
section  in  the  shape  of  knife-edges  it  is  possible  to  measure 
the  length  of  this  form  of  pendulum  (Rater's)  very  accurately. 
The  distance  between  the  knife-edges  being  the  length  of 
a  simple  pendulum  that  vibrates  in  the  same  time,  it  can  be 
substituted  for  /  in  Formula  26,  from  which 


By  substituting  also  the  time  t  determined  by  experiment, 
the  value  of  g  is  determined. 

96.  Uses  of  the  Pendulum.  —  The  most  common  use  of 
the  pendulum  is  as  a  timekeeper.  Since  the  vibrations  are 
performed  in  equal  intervals  of  time  (i.e.,  are  isochronous), 
all  that  is  needed  is  to  make  the  to-and-fro  motion  of  the  pen- 
dulum regulate  the  rotary  motion  of  the  hands.  This  is 
done  by  the  use  of  an  escapement  by  means  of  which  each 
complete  vibration  lets  one  tooth  of  a  cogwheel  escape,  so 
that  if  the  wheel  has  30  teeth,  it  will  rotate  once  while  the 
pendulum  vibrates  back  and  forth  30  times.  This  wheel  is 


THE   PENDULUM 


95 


one  of  a  train  of  cogwheels  that  move  the  hands.       The 

motion  of  the  pendulum  is  kept  up  by  a  push  from  each  cog 

as  it  escapes,  and  the  motion  of  the  train 

is  kept  up  by  the  pressure  of  a  spring  or 

by  the  pull  of  a  weight.     In  order  that 

the  times  of  vibration  may  be  equal,  the 
length  must  always  be  the 
same,  and  corrections  must 
be  made  for  the  changes  in 
length  due  to  changes  of  tem- 
perature. In  most  pendulums 
this  is  done  by  moving  the 
bob  up  or  down  by  means  of 
a  nut  running  upon  the  wire 
support.  It  is  done  auto- 
matically in  various  forms  of 
compensation  pendulums.  In 
some  of  these  two  different  sets 
of  metal  rods  are  used  so  that 
the  expansions  shall  oppose 
each  other.  In  the  mercurial 
pendulum  (Fig.  68),  glass  tubes  filled  with  mer- 
cury are  used  for  the  bob,  and  are  so  arranged 
that  the  expansions  and  contractions  of  the  mer- 
cury just  counteract  the  effect  of  the  contraction 

and  expansion  of  the  suspending  rod. 

Questions 

1.  What  force  keeps  a  pendulum  vibrating? 

2.  What  force  brings  it  to  rest  ? 

3.  Does  changing  the  weight  of  a  pendulum  bob  change  the 
time  of  vibration  ? 

4.  Does  changing  the  amplitude  change  the  time  of  vibration? 


FIG.  67 


FIG.  68 


96  THE  MECHANICS   OF  SOLIDS 

6.  Does  changing  the  lengtn  change  the  time  of  vibration  ? 

6.  State,  in  the  form  of  a  proportion,  the  relation  between  the 
numbers  of  vibrations  per  second  and  the  times  of  vibration  of  two 
pendulums. 

7.  Do  the  same  for  the  numbers  of  vibrations  and  the  lengths. 

8.  A  certain  pendulum  vibrates  twice  in  a  second.     How  many 
times  per  second  will  another  pendulum  vibrate  in  the  same  place  if 
it  is  two  and  a  quarter  times  as  long  ? 

9.  A  certain  pendulum  vibrates  once  in  one  third  of  a  second. 
What  must  be  the  relative  length  of  a  pendulum  to  vibrate  once  in 
two  thirds  of  a  second  at  the  same  place  ? 

10.  A  certain  pendulum  clock  loses  time.  How  can  it  be  made 
to  give  correct  time? 

Problems 

1.  What  must  be  the  length,  in  centimeters,  of  a  pendulum  at 
New  York  to  make  a  half  vibration  in  1^  sec.  ? 

2.  What  is  the  time  of  a  half  vibration  of  a  4-ft.  pendulum  at 
New  York? 

3.  What  is  the  length  of  a  seconds  pendulum  at  the  Smithsonian 
Institution  in  Washington,  D.C.,  10  m.  above  sea  level,  where  the 
value  of  g  is  980.1? 

4.  On  Pikes  Peak,  at  an  elevation  of  4293  m.,  the  value  of  g  is 
979.94.     Find  the  length  of  a  seconds  pendulum  there. 

5.  At  Yakutat  Bay,  Alaska,  at  an  elevation  of  4  m.,  the  length  of 
the  seconds  pendulum  is  99.479  cm.     Find  the  value  of  g  there. 

6.  Explain  the  reasons  for  the  different  values  of  g  given  in  these 
problems. 

V.    MACHINES 

97.  A  Machine  is  a  mechanical  device  used  to  apply 
force  advantageously.  If  a  machine  could  be  made  to  operate 
without  friction,  the  work  applied  by  it  would  be  exactly 
equal  to  the  work  employed  in  operating  it.  Since  it  is 
impossible  to  make  such  a  perfect  machine,  the  work  applied 
by  a  machine,  the  output,  is  always  less  than  the  work  put  into 
it,  the  input. 


MACHINES  97 

98.  Efficiency.  —  The  efficiency  of  a  machine  is  the  ratio 
of  the  work  actually  applied  by  it,  to  the  work  that  would 
be  applied  if  it  had  no  friction,  Various  devices  are  adopted 
for  increasing  this  efficiency  by  making  the  friction  as  little 
as  possible,  one  of  the  best  being  ball  bearings  such  as  are  used 
on  bicycles.  Efficiency  is  expressed  as  a  per  cent.  An 
efficiency  of  92  %  means  that  of  every  100  parts  of  total  work, 
there  are  92  parts  of  useful  work,  and  8  parts  lost  by  friction. 
The  expression  for  efficiency  is  as  follows  : 

Useful  work      Output 
Efficiency  =  ^      ,  --  =—  =  y—    —  , 
Total  work        Input 


or 


(28) 


99.  The  General  Law  of  Machines.  —  The  work  of  a 
machine  consists  in  the  overcoming  of  some  force,  which  we 
call  resistance  or  weight,  while  the  force  applied  in  operating 
the  machine  is  called  effort  or  power.  A  law  that  is  appli- 
cable to  all  machines  is  :  The  power  multiplied  by  the  distance 
through  which  it  acts  is  equal  to  the  resistance  multiplied  by 
the  distance  through  which  it  is  moved;  or, 

Pd  =  RD.  (29) 

Each  machine  has  its  own  law,  which  is  generally  more 
convenient  than  the  above.  But  this  law  is  general,  and  may 
be  applied  to  any  machine  or  combination  of  machines.  It 
is  evident  that  the  R  in  Formula  29  should  include  the  friction 
of  the  machine  as  well  as  the  resistance  to  be  overcome  in 
useful  work  ;  but  in  most  problems  in  simple  machines  we  con- 
sider only  the  conditions  of  static  equilibrium,  and  neglect  the 
friction. 

Rev. 


98  THE   MECHANICS   OF  SOLIDS 

100.  Mechanical  Advantage.  —  While  no  machine  can  give 
an  increase  in  work,  there  can  be  an  increase  in  either  speed  or 
force.  The  ratio  of  the  force  overcome  as  resistance, 
to  the  force  employed  as  power,  is  called  the  mechanical 
advantage  of  the  machine  with  respect  to  force,  provided 
this  ratio  is  greater  than  1  ;  while  the  ratio  of  the  speed 
of  the  resistance,  to  the  speed  of  the  power,  is  the  mechanical 
advantage  in  speed,  provided  this  ratio  is  greater  than  1. 
The  mechanical  advantage  is  usually  given  as  it  would  be 
if  the  machine  were  operated  without  friction. 

For  instance,  suppose  that  a  machine  moves  a  resistance  of  1000 
pounds  of  force  a  distance  of  5  feet,  and  that  the  work  needed  to 
operate  it  (in  addition  to  overcoming  the  friction  of  the  machine) 
is  a  force  of  100  pounds  moving  over  a  distance  of  50  feet.  The 
mechanical  advantage  of  force  would  be  the  ratio  of  1000  to  100; 
namely,  10.  (In  actual  operation  a  force  of  perhaps  110  pounds 
instead  of  100  would  be  required,  in  which  case  the  efficiency  would 


be  *  *    or  nearly  91  %.) 

11U   X  o\) 

For  any  increase  in  force  through  the  mechanical  advantage 
there  is  a  corresponding  decrease  in  speed,  and  for  any  in- 
crease in  speed  there  is  a  corresponding  decrease  in  force. 
This  means  again  that  there  can  be  no  gain  in  the  work 
done  through  the  use  of  a  machine. 

101.  Simple  Machines.  —  The  many  more  or  less  compli- 
cated machines  in  common  use  may  be  reduced  in  principle  to 
but  six  :  the  lever,  pulley,  wheel  and  axle,  inclined  plane, 
wedge,  and  screw.  These  are  called  the  mechanical  powers 
or  simple  machines.  These  six  simple  machines  may  be 
still  further  reduced  to  two,  the  lever  and  the  inclined  plane, 
as  it  can  easily  be  shown  that  the  pulley  and  the  wheel  and 


MACHINES  99 

axle  are  only  modified  levers,  while  the  screw  and  the  wedge 
are  modified  inclined  planes. 

102.  The  Lever  is  a  rigid  bar  that  is  capable  of  movement 
about  a  fixed  point  called  the  fulcrum.  There  are  three 
classes  of  levers,  which  are  distinguished  by  the  relative 
positions  of  the  fulcrum  and  of  the  points  of  application 
of  the  applied  force  (power)  and  R 
the  resistance  (weight). 

(a)  Levers  of  the  First  Class. — In  a 
lever  of  the  first  class  (AB,  Fig.  69) 
the  power  is  applied  at  one  end 
and  the  weight  at  the  other,  with  the 

w  FIG.  69.  —  First  Class 

fulcrum  between  them. 

The  mechanical  advantage  in  levers  of  this  class  may  be 
p      either   of   speed  or  of  force.     If  the 
F    B j^     power  arm  is  greater  than  the  resist- 
ance arm,  the   mechanical  advantage 
is  one  of  force ;  while  if  the  power  arm 
is  less  than  the  resistance  arm,  it  is  one 
of  speed. 
w  (b)  Levers  of  the  Second  Class. — In  a 

FIG.  70. -Second Class      leyer  of   ^   second  dags  (pig>  7Q) 

power  is  at  one  end  and  the  fulcrum  at  P 

the  other,  with  the  weight  between  them. 
In  levers  of  this  class  the  mechani- 
cal advantage  is  always  one  of  force. 
It  can  never  be  one  of  speed,  since 
the  resistance  arm  is  always  less  than 
the  power  arm. 


(c)  Levers  of  the  Third  Class.  —The 
lever  of  the  third  class  (Fig.  71)  has    FIG.  71.— Third  Class  W 


100  THE   MECHANICS  OF  SOLIDS 

.the  weight  at  one  end  and  the  fulcrum  at  the  other,  with 
the  power  between  them. 

The  mechanical  advantage  in  this  class  of  levers  is  always 
one  of  speed,  since  the  resistance  arm  is  greater  than  the 
power  arm. 

103.  The  Law  of  Equilibrium  of  the  Lever.  —  By  applying 
the  principle  of  moments,  we  can  readily  find  an  expression 
for  the  law  of  the  lever.  As  F  is  fixed  in  every  case,  it  is  the 
center  of  moments,  and  when  the  lever  is  in  equilibrium, 
the  moment  of  P  equals  the  moment  of  W.  Hence  P  X  AF 
=  W  X  BF.  Writing  this  as  a  proportion,  we  have 

P :  W  =  BF :  AF, 
or  Power  :  Weight  =  Weight  arm  :  Power  arm, 

in  which  "  arm  "  means  the  perpendicular  from  the  fulcrum 
to  the  direction  of  the  force.     Using  the  more  general  term 
Resistance  in  place  of  Weight,  we  write  the  formula  thus : 
Power  :  Resistance  =  Resistance  arm  :  Power  arm.  (30) 

The  mechanical  advantage  of  any  lever  is  the  ratio  of  the 
longer  arm  to  the  shorter  arm. 

If  additional  forces  are  applied  at  different  points  along 
the  lever,  equilibrium  will  be  maintained  when  the  sum  of 
the  moments  producing  clockwise  rotation  is  equal  to  the 
sum  of  the  moments  producing  counterclockwise  rotation. 
Moments  producing  counterclockwise  rotation  are  some- 
times called  positive,  and  those  producing  clockwise  rota- 
tion negative  :  if  this  is  done,  equilibrium  will  be  maintained 
whenever  the  sum  of  all  the  moments  is  zero. 

If  a  body  is  acted  on  by  a  number  of  forces  and  is  in  equi- 
librium, any  point  at  which  force  is  applied  may  be  taken 
as  the  center  of  moments,  when  the  sum  of  the  clockwise 


MACHINES 


101 


moments  with  reference  to  this  point  will  be  equal  to  the 
sum  of  the  counterclockwise  moments.  This  is  true  how- 
ever great  the  number  of  forces,  and  whether  they  are  parallel 
or  not.  If  A  in  Fig.  69  is  taken  as  the  center  of  moments, 
W  tends  to  produce  a  counterclockwise  rotation  which  is 
counterbalanced  by  the  pressure  of  the  fulcrum  upon  the 
lever,  at  F.  This  pressure  at  F  is  upward  in  direction,  and  is 
equal  to  P  +  W, 
the  pressure  that 
P  and  W  exert 
upon  the  fulcrum. 


FIG.  72.  —  Algebraic  Balance 


Demonstration.  — 
The  equality  of  mo- 
ments may  be  dem- 
onstrated by  the  use 
of  the  algebraic  bal- 
ance (Fig.  72). 

The  moments  of 
the  weights  hung  di- 
rectly on  the  bar  are  clockwise.  The  moment  of  the  weight  hang- 
ing from  the  cord  passing  over  the  fixed  pulley  is  counterclockwise. 
To  produce  equilibrium  these  must  counterbalance  each  other. 

By  different  arrangements  of  the 
weights  the  three  classes  of  levers 
can  be  illustrated. 

104.  The  Bent  Lever.  —When 
a  hammer  is  used  to  draw  a  nail, 
it  is  a  lever  of  the  first  class, 
though  the  fulcrum  is  not  in  a 
straight  line  joining  the  points  of 
application  of  the  power  and  the  resistance.  This- consti- 
tutes a  bent  lever.  The  law  of  moments  holds  for  it.  For 
Formula  30  the  "  arms  "  are  the  dotted  lines  in  Fig.  73. 


102 


THE  MSCHANICS  OF  SOLIDS 


105.  The  Common  Balance  is  a  lever  of  the  first  class  with 
equal  arms,  hence  in  this  case  P  =  IF.  In  order  that  the 
balance  may  be  accurate,  the  arms,  or  parts  of  the  beam 
on  each  side  of  the  fulcrum,  must  be  of  equal  weights  and' 
lengths.  In  order  that  it  may  be  sensitive,  the  arms  must 
be  light,  the  friction  must  be  little,  and  the  knife-edge  ful- 
crum must  be  very  close  to  a  line  joining  the  knife-edges  of 
the  scale  pans,  with  the  center  of  gravity  of  the  arms  just 
below  it. 

Even  if  a  balance  does  not  fulfill  the  conditions  for  ac- 
curacy, the  true  weight  of  a  body  may  be  found  with  it  by 
the  method  of  substitution  as  follows :  First  counterbalance 
the  body  exactly  by  putting  sand  or  any  other  convenient 
substance  in  the  other  scale  pan.  Then  remove  the  body 
and  substitute  for  it  known  weights  until  they  exactly  coun- 
terbalance the  sand.  The  sum  of  the  weights  required  will 

be  the  weight  of  the 
body. 

106.  The  Steel- 
yard (Fig.  74)  is  a 
lever  of  the  first  class 
with  unequal  arms. 
By  having  one  hook 
to  which  the  article 
•to  be  weighed  is  at- 
tached, and  two,  by  either  of  which  the  steelyard  may  be 
supported,  both  sides  of  the  bar  are  used,  one  for  light  and 
the  other  for  heavy  bodies. 

107.  The  Compound  Lever.  —  If  the  short  arm  of  one 
lever  is  made  to  work  upon  the  long  arm  of  a  second,  the 
combination  is  called  a  compound  lever.  The  mechanical 


FIG.  74 


MACHINES 


103 


advantage  is  the  ratio  of  the  product  of  the  long  arms  to 
the  product  of  the  short  arms.    The  platform  scale  (Fig.  75) 


FIG.  75.  —  Platform  Scale 

used  for  weighing  hay  and  coal  is  an  example  of  its  appli- 
cation. 

108.  The  Wheel  and  Axle  is  a  modified  lever,  the  arms 
being  the  radii  of  the  wheel  and  the  axle.  The  power  is 
usually  applied  at  the  circumference  of  the 
wheel,  and  the  weight  at  the  circumference 
of  the  axle.  In  Fig.  76  the  power  is  applied 
at  A,  the  weight  at  B,  the  fulcrum  is  at  C 
(the  center  of  both  wheel  and  axle),  and  the 
lever  arms  are  R  and  r  respectively  ;  the  ar- 
rangement is  a  modified  lever  of  the  first  class. 


109.  Law  of  the  Wheel  and  Axle.  —  Since 
the  moment  of  the  power  must  equal  the 
moment  of  the  weight  whenever  there  is  equilibrium,  we 
have,  from  Fig.  76,  PR  =  Wr  ;  or,  in  the  form  of  a  pro- 
portion, p  .  w  =  r  :  R.  (31) 

This  can  be  stated  as  follows  :  A  certain  power  applied 
to  the  wheel  and  axle  can  support  a  weight  as  many  times  greater 


104 


THE   MECHANICS  OF  SOLIDS 


than  itself  as  the  radius  of  the  wheel  is  times  greater  than  the 
radius  of  the  axle.  The  radii  in  Formula  31  can  be  replaced 
by  either  the  circumferences  or  the  diameters  if  it  is  more 
convenient. 

The  mechanical  advantage  of  the  wheel  and  axle  is  the 
ratio  of  R  to  r.     If  the  power  and  weight  are  disposed  as 

in  Fig.  76,  the  mechanical 
advantage  is  one  of  force ; 
if  the  points  of  application 
of  P  and  W  are  inter- 
changed, it  is  one  of  speed. 
The  wheel  and  axle  is 
used  to  raise  water  from 
a  well,  to  hoist  ore  from  a 
mine,  as  with  the  windlass, 
to  move  buildings,  and  to 
raise  anchors,  as  with  the  capstan.  In  the  capstan  no  wheel 
is  used,  but  instead  straight  bars,  called  hand-spikes,  are 
put  into  holes  in 
the  head  of  the  cap- 
stan, and  the  power 
is  applied  to  these. 


FIG.  77.— The  Capstan 


110.  Combina- 
tions of  the  Wheel 
and  Axle,  with  the 
axle  of  one  system 
working  upon  the 
wheel  of  another, 
are  used,  not  only  where  great  weights  are  to  be  lifted,  but 
also  where  it  is  desired  to  make  a  great  difference  in  speed 
between  the  movement  of  the  power  and  of  the  resistance. 


. 

FIG.  78. — Automobile  Transmission  Gearing 


MACHINES 


105 


These  results  are  usually  secured  by  the  use  of  a  train  of 
cog  wheels  such  as  is  shown  in  Fig.  78,  which  represents  a 
set  of  automobile  transmission  gearing. 

111.  The  Pulley.  —  The  fixed  pulley,  in  which  the  axis 
of  the  pulley  is  held  in  a  fixed  position  is  a  modified 
lever,  of  the  first  class ;  but  in  this  ma- 
chine the  power  arm  is  always  equal  to 
the  weight  arm,  so  that  there  is  no  gain  in 
using  it,  except  change  in  direction.  This 
may  be  seen  readily  by  reference  to  Fig. 
79.  The  power  is  applied  at  one  end  of  a 
rope  that  passes  around  the  pulley  in  a 
groove  cut  in  its  edge,  and  is  tangent  at  p 
the  points  A  and  B.  Apply  the  law  of 
the  lever,  and  the  proportion  will  stand 


FIG.  79 


but  r  =  R, 


P:W=  r:R-, 
.'.  P  =  W. 


(32) 


112.  The  Movable  Pulley,  in  which  the  axis  of  the  pulley 
can  move  with  it,  is  a  modified  lever,  but  it  is  of  the  second 
p-     class,  the  fulcrum  being  at  B  (Fig.  80), 
the  weight  (including  the  weight  of  the 
pulley)  being  applied  at  C  with  a  lever 
arm  CB  =  r,  and  the  power  at  A  with  a 
lever  arm  AB  =  D.     The  formula  for  the 
single  movable  pulley  is  P :  W  =  r:D, 
and  since  D  is  the  diameter  and  r  is 
the  radius  of  the  pulley,  this  becomes 


P:W  =  1:2, 


FIG.  80 


or 


(38) 


106 


THE   MECHANICS  OF  SOLIDS 


113.  Combinations  of  Fixed  Pulleys.  —  Fig- 
ure 81  shows  how,  by  a  combination  of  fixed 
pulleys,  the  horizontal  pull  of  a  horse  can  be 
used  to  raise  a  heavy  weight.  The  mechanical 
advantage  secured  by  the  movable  pulley 
would  frequently  be  useless  if  it  were  not  for 
combining  with  it  one  or  more  fixed  pulleys  by 
which  the  direction  of  the 
pull  can  be  changed. 


114.  Systems  of  Fixed 
and  Movable  Pulleys.  -  FlG  81 

Where  great  weights  are 

to  be  raised,  systems  of  pulleys  are  used.  Usually  a  num- 
ber of  "  sheaves  "  or  pulleys  are  arranged  side  by  side  in  the 
same  block,  and  a  single  rope  is  ^.^^^ 
passed  alternately  around  the 
sheaves  in  two  of  these  blocks,  called 
the  "block  and  tackle"  (Fig.  82). 
Another  arrangement  is  shown  in  Fig. 
83.  The  weight  is  attached  to  the 
movable  block  A  (Figs.  82  and  83),  and 
since  the  rope  is  continuous  there  must 
be  the  same  pull  on  each  branch  be- 
tween the  blocks.  If  we  let  n  represent 
the  number  of  branches  extending  to 
the  movable  block  (n=  6  in  Figs.  82  and 
83),  then  by  §  62  each  branch  must 


p 


support  -  of  the  weight; 

P=E. 

n 


(34) 


•ft 

FIG.  83 


MACHINES 


107 


108 


THE  MECHANICS   OF  SOLIDS 


115.'  The  Inclined  Plane.  —  Any  plane  surface  that  makes 
an  angle  with  a  horizontal  surface  forms  an  inclined  plane. 
A  ball  placed  upon  a  horizontal  plane  will  retain  its  position 
and  will  press  upon  the  plane  with  its  entire  weight.  As 
soon,  however,  as  one  end  of  the  plane  is  raised,  the  entire 
weight  of  the  ball  will  not  rest  upon  the  plane,  and  it  will 
begin  to  roll  toward  the  lower  end.  The  only  way  in  which 
an  inclined  plane  can  be  used  efficiently  is  to  have  the  moving 


FIG.  85 

force  act  in  a  direction  that  is  parallel  to  the  inclined  surface 
of  the  plane.  Inclined  planes  are  used  for  the  purpose  of 
lifting  a  weight  to  a  certain  height  by  the  use  of  a  small  power. 
The  power  which  moves  a  body  from  the  bottom  of  the  plane 
to  the  top  lifts  it  through  the  height  of  the  plane  against 
gravity  and  hence  the  general  law  of  machines  will  apply. 
This  may  be  modified  to  read 

PL  =  WH,  whence  P :  W  =  II :  L,  (35) 

in  which  H  is  the  vertical  height  of  the  plane  and  L  is  the 
length  along  the  slope. 


MACHINES 


109 


A  demonstration  of  the  law  of  the  inclined  plane  can  be 
made  with  an  apparatus  like  that  shown  in  Fig.  85.  The 
cylinder  is  the  weight  and  the  pull  of  the  power  is  made 
parallel  to  the  plane  by  means  of  the  cord  running  over  the 
fixed  pulley  at  the  top. 


FIG.  86 


.  The  Wedge  is  nothing  more  than  a  modified  inclined 
plane.  It  is  generally  made  with  its  base  (which  corresponds 
to  the  height  of  an  inclined  plane)  perpen- 
dicular to  a  line  drawn  from  the  edge  to 
the  middle  of  the  base.  This  means  that 
it  is  made  of  two  inclined  planes  placed 
base  to  base.  The  power  is  usually  ap- 
plied by  the  blow  of  a  heavy  body. 
Wedges  are  used  in  splitting  logs  and 
stone,  raising  heavy  weights  a  short  distance,  launching 
ships,  and  similar  operations. 

117.  The  Screw  consists  of  a  cylinder  of  wood  or  metal 
about  which  is  a  thread.  If  the  cross  section  of  this  thread 
is  square,  the  thread  is  called  a  square  thread  ;  if  triangular, 
it  is  called  a  V-thread.  A  good  model  of  a  square-thread 

screw  can  be  made  by  winding  a 
long  strip  of  leather  in  a  spiral 
around  a  wooden  cylinder,  and 
tacking  it  fast. 

That  the  screw  is  a  modified  in- 
clined plane  may  be  seen  by  cut- 
ting a  right-angled  triangle  out 
of  paper  and  winding  it  about  a 
pencil  as  in  Fig.  88.  It  will  be 

seen  that  the  hypotenuse,  which  represents  the  length  of  an 
inclined  plane,  forms  the  spiral  thread  of  the  screw.    If 


Square  Thread  V-thread 

FIG.  87.  — Screws 


110 


THE  MECHANICS  OF  SOLIDS 


CB   is  taken  equal  to  the  circumference  of   the 
pencil,    then    AB  will   be  equal  to   the   distance 
between  the  threads  DE.     This  distance  is  called 
the  pitch,  and  determines  how  far  the  screw  (or 
the    resistance)  moves  at  each  revolution.      The 
power  is  generally  applied  to  a 
screw   at   the  end  of  a  lever, 
as  the  handle  of  a  wrench.     It 
is  applied   either  to  the   screw 
or  to  the  nut,  as  in  bolting  two 
pieces  of  wood  together. 


FIG.  88 


118.  The  Law  of  the  Screw.  -  -  The  mechanical  advantage 
of  a  screw  cannot  be  determined  unless  we  know  at   what 
point  the  power  is  applied.     From  the  gen- 
eral  law   of   machines,  the  formula  can  be 
written  P  X  2  TrR  =  Wp,  or 

P:W  =  p:2  TrR,  (36) 

in  which  p  is  the  pitch  of  the  screw,  and  R 
is  the  radius  of  the  circle  through  which  the 
power  moves. 


FIG.  89.  — Lifting 
Jack 


119.  Application  of  the  Screw.  —  Lifting 
jacks,  cotton  and  hay  presses,  the  screw  pro- 
peller of  ships,  and  air  fans  are  familiar  examples  of  the  prac- 
tical uses  to  which  the 
screw  is  put,  besides 
the  constant  use 
that  is  made  of  it 
machinery  and 


in 


woodworking.       The 
spherometer  and  mi- 


FIG.  90 


MACHINES  111 

crometer  screw  are  examples  of  its  use  in  scientific  work. 
The  speed  counter  shown  in  Fig.  90  shows  how  an  endless 
screw,  meshing  into  teeth  on  the  circumference  of  a  wheel, 
can  be  used  to  determine  the  rotation  of  an  axle,  the 
pointed  end  of  the  screw  being  thrust  into  a  hole  in  the  end 
of  the  axle  and  rotating  with  it. 

120.  Friction.  —  Whenever  any  body  is  put  in  motion  by 
sliding  or  rolling  it  over  another,  and  the  body  is  then  left 
to  itself,  its  velocity  will  gradually  diminish,  and  it  will  come 
to  rest.     This  is  due  to  friction,  which  is  the  resistance  that 
is  encountered  in  moving  (or  trying    to  move)   one  body  over 
another  under  pressure.     Friction  arises  from  inequalities  in 
the  surfaces  in  contact.     If  any  means  is  taken  to  reduce 
these  inequalities,  either  by  making  the  surfaces  smoother, 
or  by  filling  up  the  depressions  with  some  form  of  lubricating 
material,  the  friction  is  diminished. 

121.  Laws  of  Sliding  Friction.  —  Experiment  has  estab- 
lished the  following  law  for  sliding  friction  —  both  for  fric- 
tion of  motion  and  for  friction  of  rest  : 

Sliding  friction  is  proportional  to  the  pressure,  and  inde- 
pendent of  the  extent  of  the  surfaces  in  contact.  It  varies  with 
the  character  of  the  surfaces. 

Within  certain  limits  friction  of  motion  is  also  independ- 
ent of  the  velocity  of  the  motion. 

122.  Coefficient  of  Friction.  —  The  coefficient,  or  measure, 
of  sliding  friction  —  either  of  rest  or  of  motion  —  is  ex- 
pressed by  the  equation 

f='  (37) 


112 


THE  MECHANICS  OF  SOLIDS 


FIG.  91 


in  which  P  is  the  force  necessary  to  overcome  the  friction, 
and  W  is  the  pressure  normal  (perpendicular)  to  the  surfaces 

in  'contact.  A  simple 
method  of  determining 
this,  for  friction  of  rest, 
is  to  place  a  block  of 
known  weight,  W,  upon 
a  level  board,  and  set 
p  it  in  motion  by  putting 
weights  in  a  scale  pan 
suspended  as  in  Fig.  91.  In  measuring  friction  of  motion 
care  must  be  taken  that  the  speed  is  uniform/ 

123.  Rolling  Friction.  —  If  two  equal  masses  of  iron  are 
drawn  over  a  smooth  iron  surface,  one  being  in  the  form  of 
a  block  with  a  flat  base  and  the  other  in  the  form  of  a  cylinder 
so  arranged  as  to  roll,  it  will  be  found  that  the  cylinder  offers 
much  less  resistance  to  the  motion  than  the  block  does. 
Rolling  'friction  depends  upon  the  hardness  and  smoothness 
of  the  surfaces  in  contact.  When  these  are  very  hard  and 
smooth,  rolling  friction  is  much  less  in  amount  than  sliding 
friction  —  as  in  the  case  of  a  car  wheel  running  on  a  steel 
track.  If,  however,  the  surface  over  which  a  wheel  rolls  is 
soft  and  yielding, 
as  in  the  case  of  a 


be  even  greater  than 
sliding  friction.  In 
such  a  case  the 


FIG.  92.  —  Ball  Bearings 


wheel  has  to  be  constantly  climbing  the  hill  caused  by  the 
sinking  of  the  wheel  in  the  sand.     If  the  wheel  is  yielding, 


MACHINES     -  113 

as  in  the  case  of  an  automobile  tire  that  is  not  well  filled 
with  air,  the  wheel  is  flattened  at  the  point  of  contact, 
thus  increasing  the  rolLng  friction. 

The  efficiency  of  machines  is  increased  by  changing  sliding 
friction  to  rolling  friction,  by  the  use  of  hardened  steel  cylin- 
ders or  balls  placed  between  the  axle  and  the  bearing.  In 
roller  bearings,  the  contacts  are  line  contacts,  while  in  ball 
bearings,  they  are  point  contacts. 

124.  Advantages  of  Friction.  —  While  all  possible  means 
are  taken  to  reduce  the  friction  between  the  parts  of  a  ma- 
chine that  move  over  each  other,  friction  has  many  advan- 
tages. The  difficulty  of  walking  on  an  icy  pavement  illus- 
trates the  decrease  of  stability  that  comes  with  a  decrease  of 
friction.  The  stability  of  the  ceiling  of  a  room  is  dependent 
upon  the  friction  between  the  lath  nails  and  the  joists. 
Horses  that  easily  draw  a  heavy  load  over  a  dry  pavement 
will  fall  when  the  pavement  is  wet.  The  ability  of  a  locomo- 
tive engine  to  haul  its  train  is  due  to  the  friction  between 
the  driving  wheels  and  the  rails.  If  the  rails  are  wet,  the 
wheels  slip  until  sand  is  sifted  over  the  rails. 

Questions 

1.  Is  a  perpetual  motion  machine  possible?    Why? 

2.  What  effect  upon  the  efficiency  of  a  machine  does  it  have  to 
reduce  its  friction? 

3.  State  the  general  law  of  machines. 

4.  Name  three  machines  in  which  the  mechanical  advantage 
is  one  of  speed.     Which  is  greater  in  each  case,  the  power  used 
or  the  resistance  overcome? 

5.  What  point  is  the  center  of  moments  in  a  lever? 

6.  Draw  a  figure  of  a  lever  of  the  first  class,  in  which  the  moment 
of  the  power  and  the  moment  of  the  weight  shall  each  be  80. 

Rev. 


114  THE   MECHANICS  OF  SOLIDS 

7.  With  which  class  of  lever  will  a  force  of  100  Ib.  raise  the 
greatest  weight,  the  lever  being  12  ft.  long  and  the  weight  arm  2  ft. 
long?    Prove  your  answer  by  a  figure. 

8.  Which  class  of  lever  is  represented  by  a  pair  of  shears  ?   Sugar 
tongs  ?    A  wheelbarrow  ?    An  oar  in  rowing  a  boat  ? 

9.  A  ladder  lies  upon  the  ground  with  its  foot  against  a  house. 
Show  by  a  figure  how  it  changes  from  one  class  of  lever  to  another 
when  a  man  takes  it  by  the  top  and  raises  it  slowly  to  a  vertical 
position  by  lifting  successively  on  rungs  nearer  and  nearer  the  foot. 

10.  Locate  the  positions  of  the  power,  fulcrum,  and  resistance  in 
a  pair  of  sugar  tongs,  a  pair  of  blacksmith's  tongs,  a  loaded  pitch- 
fork. 

11.  Why  does  moving  the  fulcrum  nearer  a  stone  to  be  raised 
make  it  easier  to  raise  the  stone  with  a  crowbar  ? 

12.  In  what  class  of  lever  is  the  weight  a  help  ?    In  what  class  a 
hindrance  ? 

13.  With  a  given  length  of  handspike  would  you  choose  a  capstan 
with  a  large  or  small  barrel  for  raising  a  heavy  anchor? 

14.  Which  would  you  choose  if  you  wanted  to  raise  it  quickly? 

15.  How  much  can  a  man  raise  with  a  single  fixed  pulley? 

16.  Would  you  prefer  to  roll  a  barrel  of  flour  into  a  wagon  up  a 
plank  used  as  an  inclined  plane  or  to  push  a  box  of  equal  weight 
up  the  plank?    Why? 

17.  In  what  way  is  friction  between  the  tires  of  an  automobile 
and  the  road  helpful?     In  what  way  is  it  harmful? 

Problems 

1.  What  is  the  efficiency  of  a  machine  in  which  10%  of  the 
power  is  lost  in  overcoming  the  friction? 

2.  What  is  the  efficiency  of  a  machine  with  which  a  power  of  25 
Ib.  moving  30  ft.  can  move  a  resistance  of  130  Ib.  of  force  through 
a  distance  of  5  ft.  ? 

3.  In  a  lever  of  the  first  class  a  force  of  25  Ib.  balances  a  load  of 
275  Ib.    The  force  arm  is  2.2  ft.    Find  the  load  arm.    What  is  the 
mechanical  advantage? 

4.  Make  a  drawing  of  a  lever  of  the  second  class  in  which  a 
force  of  25  Ib.  supports  a  load  of  275  Ib. 


MACHINES 


115 


25 


FIG.  93 


40 


6.  In  Fig.  93  the  numbers  on  the  lever  represent  distances 
from  the  fulcrum  in  feet,  and  the  numbers  at  the  arrow  points 
represent  pounds  of  force.  Where  lg 

must  a  force  of  36  Ib.  be  applied    e     f    F  1  20 

to  put  the  system  shown  in  equi- 
librium, if  we  assume  that  the 
lever  by  itself  will  balance  on 
Fl  .What  will  be  the  amount 
and  directions  of  the  pressures 
at  F? 

6.  What  will  be  the  answers  in  problem  5  if  the  lever  weighs 
2   Ib.    per   running  foot   so   that   it   will   not   by  itself    balance 
on*'? 

7.  A  filbert  is  placed  three  quarters  of  an  inch  from  the  hinge 
of  a  nutcracker  while  the  hand  is  5  in.  from  the  hinge.     What 
pressure  acts  upon  the  filbert  when  the  hand  presses  2  Ib.  ? 

8.  A  man  lifts  25  Ib.  of  hay  with  a  pitchfork  5  ft.  long,  by  placing 
his  right  hand  at  the  end  of  the  handle  and  his  left  hand  3  ft.  from 
the  end.     How  much  must  he  lift  with  his  left  hand? 

9.  A  boy  who  can  lift  100  Ib.  tries  to  raise  the  end  of  a  250-lb. 
iron  bar  lying  on  the  ground.     How  much  must  a  second  boy  lift  so 
that  together  they  can  raise  the  end  from  the  ground? 

10.  A  man  uses  a  pinch  bar  for  starting  a 
freight  car.     The  distance  from  the  end  of  the 
bar  to  the  bend  that  rests  on  the  rail  is  4  ft. 
and  9  in.    The  distance 
from   the    bend  to  the 
point  that   touches  the 
wheel  is  3  in.     What  is 
the    mechanical    advan- 

FIG.  94.  —  Pinch  Bar  taSe  of  the  bar >  and  ^OW 

great   a   force  does   the 

man  exert  upon  the  wheel  when  he  pushes  with  a  force  of  75  Ib.  at 
the  end  of  the  bar  ? 

11.  A  wooden  beam  weighing  55  Ib.  per  cubic  foot  is  used  to  pry 
up  a  block  of  stone.  How  much  does  it  help  to  lift  the  stone  if  it  is 
12  ft.  long,  8  in.  square,  and  the  fulcrum  is  1  ft.  6  in.  from  the  end 
under  the  stone? 


116 


THE    MECHANICS    OF    SOLIDS 


12.  The  crank  of  a  grindstone  is  9.5  in.  long  and  the  diameter  of 
the  stone  is  22.5  in.     What  resistance  at  the  rim  of  the  stone  will  be 
balanced  by  a  force  of  12.5  Ib.  at  the  crank  handle? 

13.  A  wheel  of  a  wheel  and  axle  is  25  in.  in  circumference.     What 
must  be  the  circumference  of  the  axle  if  a  pull  of  8  Ib.  on  the  wheel 
is  to  balance  the  pull  of  a  36  Ib.  pail  suspended  from  the  axle? 

14.  The  drum  of  a  winch  is  2^  ft.  in  diameter,  and  the  shaft  1  ft. 
in  diameter.     What  must  be  the  pull  on  a  rope  wound  around  the 
drum  to  balance  the  pull  of  a  2000-lb.  rock  being  lifted  by  the  rope 
wound  around  the  shaft? 

15.  A  wheel  w  turns  10  times 
per  second  and  is  10  in.  in  diam- 
eter.' This  is  belted  to  a  shaft 
S,  6  in.  in  diameter,  upon  which 
there  is  fixed  a  wheel  W,  24  in. 
in  diameter.  What  is  the  speed 
FIG.  95  °f  a  point  on  the  circumference 

of  Wl 

16.  The  wheel  of  a  wheel  and  axle  is  3  ft.  and  the  axle  6  in.  in 
diameter.     How  many  times  must  the  wheel  turn  per  minute  to  raise 
a  weight  suspended  from  the  axle  at  the  rate  of  100  ft.  per  minute? 

17.  Two  cogwheels  that  mesh  into  each  other  have  8  and  44  teeth 
respectively.     What  is  the  relative  rate  of  rotation  of  tjie  wheels? 

18.  In  the  steelyard 
shown   in   Fig.   96,   the 
distance   from   the   ful- 
crum to  the  parcel  hook 
is  2^  in.    How  far  must 
the  weight  w  be  from 
the  fulcrum  if  it  weighs 
6    oz.    and    the    parcel 
weighs  3  Ib.? 

19.  A  capstan  (Fig.  77)  with  a  barrel  10  in.  in  diameter  is  used  to 
raise  a  500-lb.  anchor  from  a  depth  of  100  ft.  The  handspikes  are  3  ft. 
long,  measured  from  the  middle  of  the  barrel,  and  each  man  pushes 
at  a  point  4  in.  from  the  end.     How  much  must  each  of  two  men 
push  to  raise  the  anchor,  if  the  friction  increases  the  load  25%, 
and  how  far  will  each  one  walk? 


FIG.  96.  —  Steelyard 


MECHANICS 


117 


20.  A  horse  pulling  on  the  rope  of  Fig.  81  raises  a  weight  of  500 
Ib.  to  a  height  of  12  ft.     The  friction  increases  the  load  10%.     How 
much  must  the  horse  pull  and  how  far  must  he  walk? 

21.  What  is  the  pull  supported  by  the  rope  of  a  block  and  tackle 
of  three  pullejrs  in  the  movable  block  and  three  pulleys  in  the  fixed 
block,  when  the  weight  supported  is  624  kg.?    How  far  must  the 
power  move  to  raise  the  weight  3m.? 

22.  Suppose  the  rope  to  be  fastened  to  the  movable  block  men- 
tioned in  problem  21  and  one  more  pulley  to  be  added  to  the  fixed 
block.     How  many  branches  of  rope  will  extend  to  the  movable 
block?     Make  a  drawing  to  show  the  arrangement,  and  compute 
the  pull  on  each  rope. 

23.  An  inclined  plane  is  13  ft.  long  and  3  ft.  high.     What  is  the 
mechanical  advantage  of  the  plane?     What  force  acting  parallel  to 
its  length  would  be  required  to  pull  a  car  weighing  156  Ib.  up  the 
incline  if  there  were  no  friction? 

24.  The  length  of  an  inclined  plane  is  300  ft.  and  its  height  25 
ft.     What  force  parallel  to  the  length  of  the  plane  is  required  to  draw 
a  loaded  truck  weighing  5  short  tons  up  the  plane  if  the  friction 
increases  the  load  10%? 

25.  A  wagon  weighing  750  Ib.  is  loaded  with  1  ton  (2240  Ib.)  of 
coal.    Besides  overcoming  friction,  how  much  must  a  horse  pull  to 
draw  the  wagon  and  coal  up  a  hill  200  ft.. long  and  40  ft.  high?     What 
horse  power  is  developed  by  the  horse  if  the  work  is  done  in  2  min.? 

26.  Neglecting  friction, 
what  horse  power  is  devel- 
oped by  a  3000-lb.  auto- 
mobile  going  up  a   10% 
grade  at  30  mi.  per  hr.? 

27.  How    much    pres- 
sure,   neglecting   friction, 
is  brought  to  bear  upon, 
a  book  in  a  letter  press, 
if  the  threads  are   £   in. 
apart   and   the   diameter 
of  the  hand  wheel  is  14 
in.,  when  the  pull  on  the 
rim  is  10  Ib.? 


FIG.  97.  —  Letter  Press 


118  THE   MECHANICS   OF   SOLIDS 

28.  A  screw  having  40  threads  to  the  inch  has  a  head  2  in.  in 
diameter.  At  what  speed  is  the  screw  moved  when  it  is  turned 
around  once  in  three  seconds?  What  is  the  speed  of  a  point  on  the 
circumference  of  the  head? 


FIG.  98.  —  Turnbuckle 

29.  This  turnbuckle  has  16  threads  to  the  inch.    The  ends  of 
the  rods  to  which  it  is  threaded  are  1  in.  apart.    How  far  apart 
are  they  after  6  complete  turns? 

30.  A  jackscrew  with  a  pitch  of  one  half  inch  has  a  handle  2  ft. 
long.     Neglecting  friction,  how  much  pressure  will  a  pull  of  75  Ib. 
at  the  end  of  the  handle  produce  at  the  end  of  the  screw?     How  far 
will  the  end  of  the  screw  move  when  the  end  of  the  handle  passes  over 
a  distance  of  10  ft.? 

31.  What  is  the  coefficient  of  friction  if  a  force  of  7  Ib.  is  required 
to  draw  a  sled  weighing  150  Ib.  at  a  uniform  speed? 

32.  A  piece  of  cast  iron  weighing  125  Ib.  was  pulled  across  a  con- 
crete floor  at  a  uniform  speed  by  a  pull  of  45  Ib.    What  was  the 
coefficient  of  friction? 

33.  A  cake  of  ice  weighing  192  Ib.  was  pulled  across  the  ice  on  a 
lake  by  a  pull  of  24  Ib.    What  was  the  coefficient  of  friction? 


CHAPTER  IV 
LIQUIDS 

I.     MOLECULAR  FORCES  IN  LIQUIDS 

125.  Cohesion,  in  liquids,  is  the  mutual  molecular  attraction 
of  the  particles  of  a  liquid  for  one  another.  Since  water  is 
the  most  common  liquid,  the  demonstrations  that  follow 
will  be  made  with  water  unless  there  is  a  special  reason  for 
using  some  other  liquid. 

If  a  glass  rod  is  dipped  in  water  and  then  removed,  a  drop 
will  form  on  the  end  of  the  rod  and  will  grow  larger  and 
larger  as  the  water  runs  down  the  side  until  the  weight 
of  the  drop  becomes  great  enough  to  break  it  away  from  the 
rod,  when,  as  it  falls,  it  takes  the  form  of  a  sphere.  In  this 
experiment  cohesion  does  two  things:  it  keeps  the  water 
from  falling  as  soon  as  it  runs  down  the  side 
of  the  rod ;  and  it  gives  the  drop  the  form 
of  a  sphere. 

The  spherical  form  of  liquids  can  be  studied  by 
making  a  mixture  of  alcohol  and  water,  using 
such  proportions  that  the  mixture  will  have  the 
same  density  as  olive  oil.  Introduce  a  small 
quantity  of  the  oil  below  the  surface  of  the  mix- 
ture, by  the  use  of  a  glass  tube,  and  the  oil  will 
assume  the  globular  form,  as  in  Fig.  99. 

Shot  are  formed  by  pouring  molten  lead  through  sieves  at  the  top 
of  a  high  tower;  the  lead  is  thus  separated  into  small  masses, 
each  of  which  assumes  the  form  of  a  sphere. 

Demonstration.  —  Cover  a  smooth  board  with  lycopodium 
powder  or  powdered  lampblack.  Drop  a  small  quantity  of  water 

119 


120 


LIQUIDS 


upon  it  from  a  height  of  2  or  3  ft.,  and  the  water  will  scatter  and 
take  the  form  of  spheres. 

NOTE.  —  Lycopodium  powder  —  which  is  made  up  of  the  spores 
from  certain  plants  —  can  be  obtained  from  any  drug  store.  A 
few  cents'  worth  will  be  found  very  useful  for  many  experiments. 

126.  Surface   Phenomena.  —  Demonstrations.  —  Make    one 
end  of  a  small  brass  wire  very  sharp,  and  bend  it  into  the  form  of  a 

I  hook.     Put  the  hook  into  a  glass  of  clean 

water  so  that  the  point  shall  be  below  the 
surface.  Bring  the  point  of  the  hook  up  to 
the  surface,  and  observe  that  the  point,  be- 
fore breaking  through  the  surface,  lifts  it  as 
FIG.  100  ^  ft  were  a  tj1jI1  flexjbie  blanket  stretched 

over  the  water.    Observe  that  the  reflection  seen  from  the  sur- 
face of  the  water  is  distorted  at  the  point 

where  the  hook  lifts  the  surface. 

Bend  a  wire  into  the  shape  shown  at  A 

(Fig.  101).    Place  a  sewing  needle  in  the  hook 

and  lay  it  carefully  upon  the  surface  of  clean 

water,  and  the  needle  will  float   in  a  little 

depression  upon  the  surface,  as  shown  in  the 

lower  part  of  the  figure.      If  the  needle  is 

placed  below  the  surface,  it  will  sink  at  once. 

NOTH.  —  In  all  experiments  on  liquid  sur- 
faces great  care  must  be  taken  to  keep  the 
water,  and  everything  that  comes  in  contact  with  it,  clean.  The 
touch  of  a  greasy  finger  is  enough  to  change  the  surface  tension 
of  the  water. 

Certain  insects  make  use  of  the  above  phenomena  and  are 
able  to  run  over  the  surface  of  water,  their  feet  resting  in 
depressions  in  its  surface  just  as  the  needle  does. 

127.  Surface   Tension.  —  Let   us   study   the   attractions 
acting  upon  a  molecule  at  different  distances  from  the  sur- 
face, as  shown  in  Fig.  102.     At  A  the  molecule  is  attracted 


FIG.  101 


MOLECULAR  FORCES  IN  LIQUIDS  121 

equally  in  all  directions  by  the  molecules  that  are  within 
the  distance  of  molecular  attraction  (cohesion) ;  hence  it  can 
move  readily  in  any  direction.  At  B,  very  near  the  surface, 
the  horizontal  attractions  are 
equal  in  all  directions,  but  the 
inward  (downward)  attraction 
is  greater  than  the  outward 
(upward) .  At  the  surface  the 
molecule  C  has  no  outward 


attraction,  and  hence  it  is  held  FIG  102 

in  place  by  the  inward  force. 

As  this  is  true  of  every  molecule  on  the  surface,  the  result 
is  a  tension  upon  the  surface  layer  much  greater  than  upon 
any  other  layer.  The  inward  attraction  tends  to  pull  each 
molecule  in  from  the  surface  layer,  but  if  a  molecule  were 
drawn  into  the  interior  of  the  liquid,  it  would  displace  some 
other  molecule  and  force  it  to  the  surface  against  a  similar 
attraction;  so  there  is  no  change  unless  the  shape  of  the 
liquid  body  can  be  changed  so  as  to  decrease  the  area  of  the 
surface.  The  surface  tension  causes  a  tendency  of  the  surface 
to  contract  to  the  smallest  area  possible.  This  is  the  reason 
why  liquids  take  the  spherical  form  (§  125) ;  a  sphere  has  a 
smaller  surface  than  any  other  form  of  solid  of  the  same  volume. 
Surface  tension  varies  with  the  liquid  and  with  the  tem- 
perature of  the  liquid.  The  surface  tension  of  pure  water, 
which  is  very  great,  compared  with  that  of  most  other 
liquids,  is  illustrated  by  the  following : 

Demonstrations.  —  Pour  some  hot  water  into  a  shallow  dish, 
like  a  soup  plate.  Cover  the  surface  with  pepper.  Hold  a  small 
piece  of  butter  in  the  surface  of  the  water  at  the  middle,  and  observe 
how  the  pepper  goes  away  from  the  melting  butter  to  the  sides  of 
the  plate. 


122 


LIQUIDS 


Spread  a  thin  layer  of  clean  water  upon  a  clean  glass  plate,  and 
then  let  a  drop  of  alcohol  fall  upon  the  middle  of  it.  The  water 
will  at  once  retreat,  leaving  a  space  around  the  drop  of  alcohol. 
Why? 

Viscous  liquids  are  stronger  than  water  though  their  sur- 
face tension  is  less,  and  for  this  reason  oil  is  sometimes 
thrown  upon  the  water  around  a  ship  during  a  storm.  The 
effect  of  this  is  to  smooth  out  the  surface  as  though  a  strong 
elastic  blanket  were  stretched  over  the  water;  and  the 
waves  are  then  kept  from  breaking  over. 

A  drop  of  kerosene  placed  upon  water  has  less  surface 
tension  than  the  water  and  hence  is  pulled  out  by  the  tension 
of  the  water  into  a  thin  circular  film. 

128.  Films.  —  If  we  make  the  thickness  of  the  liquid 
mass  very  little,  and  give  to  it  two  free  surfaces,  surface 
tension  may  be  studied  to  better  advantage. 

Demonstrations.  —  Make  a  strong  solution  of  soap  by  dissolving 
castile  soap  in  water  until  a  large  bubble  can  be  blown.  Bend  a 
A  n  piece  of  iron  wire  so  as  to  form 

an  open  frame  with  a  handle,  and 
from  one  side  of  the  frame  hang 
a  loop  L  made  of  one  strand  of 
a  silk  thread.  Dip  this  frame 
in  the  soap  solution,  and  the 
loop  will  hang  as  at  A  in  Fig.  103. 
Remove  the  film  within  the  loop 
by  touching  it  with  the  point  of 
a  piece  of  blotting  paper,  and 
the  loop  will  at  once  spring  out 
into  the  form  of  a  circle,  as  at 
B.  Why? 

Using  a  clay  pipe  or  a  glass  tube,  blow  a  small-sized  bubble. 
Remove  the  tube  from  the  mouth,  and  hold  the  end  of  it  toward  the 


FIG.  103 


MOLECULAR  FORCES  IN  LIQUIDS  123 

flame  of  a  lighted  candle.  The  pressure  exerted  by  the  surface 
tension  of  both  sides  of  the  film  will  force  out  a  current  of  air  strong 
enough  to  blow  the  flame  to  one  side.  What  change  takes  place  in 
the  size  of  the  bubble  ? 

129.  Adhesion  between  Liquids  and  Solids.  -  •  Let  us  con- 
sider what  may  happen  when  a  solid  is  brought  into  con- 
tact with  a  liquid.  If  a  lump  of  sugar  is  dipped  into  water, 
the  adhesion  between  the  two  is  greater  than  the  cohesion 
of  the  sugar,  and  the  sugar  is  dissolved.  If  a  clean  glass  rod 
is  dipped  into  pure  water,  the  adhesion  is  greater  than  the 
cohesion  of  the  water,  and  the  rod  will  be 
found  wet  when  it  is  removed.  If  the  glass 
rod  is  dipped  into  mercury,  the  adhesion  is 
less  than  the  cohesion,  and  none  of  the  mer-  H§5 
cury  will  cling  to  the  rod. 

JL  .  FIG.  104 

When  the  glass  rod  is  dipped  into  mercury, 
the  surface  of  the  liquid  is  not  broken,  but  extends  down 
beside  and  below  the  rod.     The  surface  tension,  tending  to 
decrease  the  area  of  this  surface,  rounds  off  the  corners  at 

A  and  B,  Fig.  104,  convex  up- 
ward.     When  the  rod  is  dipped 
6g    into   water    (Fig.   105),  the  ad- 
._i§    hesion    causes    the    water   next 
the  glass  to  rise  above  the  gen- 
Fia105  eral   level,   so  that  .the  surface 

would  be  as  at  A  if  it  were  not  for  the  surface  tension ;  but 
the  surface  tension  decreases  the  area  of  the  surface  by 
rounding  off  the  corners  as  at  B,  concave  upward. 

If  two  plates  of  glass  are  thrust  into  water  with  their  faces 
parallel  to  each  other,  the  liquid  will  rise  between  them,  the 
height  being  greater,  the  nearer  the  plates  are  to  each  other. 
If  the  plates  are  held  tightly  together  at  one  edge  and  slightly 


124 


LIQUIDS 


separated  at  the  other,  as  in  Fig.  106,  this  varying  height 
will  be  shown  in  the  form  of  a  curve,  highest  at  the  angle, 

and  lowest  at  the  out- 
side edge.  This  can  be 
seen  better  if  the  water 
is  slightly  colored. 

Demonstrations.  — Pour 
some  clean  water  into  a 
beaker,  and  thrust  one  end 
of  a  piece  of  clean  glass 
tubing  below  the  surface  of 
the  water.  The  water  will 
rise  on  the  inside  of  the  tube 
to  a  considerable  height 
above  the  water  in  the 
beaker.  On  removing  the 

tube  it  will  be  found  to  be  wet.       Repeat  the  experiment  with  a 
tube  of  half  the  diameter,  and  the  water  will  rise  twice  as  high. 

Pour  clean  mercury  into  a  dish,  and  repeat  the  experiment, 


FIG.  106 


FIG.  107 


FIG.  108 


using  clean  glass  tubes  of  the  same  sizes  as  before.  Observe  that  the 
surface  of  the  mercury  is  convex  and  that  it  is  depressed  in  the  tubes. 
Notice  also  that  the  glass  tubes  are  not  wet  by  the  mercury. 

130.  Capillary  Tubes.  —  The  tubes  used  in  the  preceding 
demonstrations  —  if  very  small  —  have  received  the  name 
of  capillary  tubes,  from  the  Latin  word  capillus,  which 
means  "  hair."  The  attraction  which  causes  liquids  to  go 


MOLECULAR  FORCES  IN  LIQUIDS  125 

up  into  minute  openings  is  sometimes  called  capillary  attrac- 
tion. It  is  really  only  adhesion  and  surface  tension.  The 
water  rises  a  little  at  the  sides  of  a  glass  tube,  and  surface 
tension  first  makes  the  surface  concave  upward,  and  then 
tends  to  decrease  the  area  of  the  surface  by  flattening  the 
curvature.  This  draws  the  water  level  up  higher  inside  the 
tube-,  and  the  process  continues  until  the  adhesion  and  sur- 
face tension  are  counterbalanced  by  the  weight  of  the  column 
of  water  above  the  general  level. 

Experiment  has  established  the  following  laws : 

I.  When  a  liquid  wets  the  surface  of  a  tube  placed  in  it, 
the  surface  of  the  liquid  will  be  concave,  and  the  liquid   will 
rise  in  the  tube.     When  the  liquid  does  not  wet  the   tube,  the 
surface  of  the  liquid  will'  be  convex,  and  the  liquid  will  be  de- 
pressed in  the  tube. 

II.  The  elevation  or  the  depression  varies  inversely  as  the 
diameter  of  the  tube. 

III.  The  elevation  or  the  depression  decreases  as  the  tem- 
perature rises. 

Demonstrations.  —  Draw  from  a  piece  of  soft  glass  tubing  a 
fine  capillary  tube.  Break  out  a  piece  about  a  foot  long,  having  a 
uniform  diameter,  and  put  one  end  in  water.  Moisten  the  inside  of 
the  tube  by  drawing  it  full  of  water  and  blowing  it  out  again.  Hold 
the  tube  vertically  and  measure  the  height  of  the  water  in  it.  Draw 
the  tube  gently  from  the  water  and  notice  whether  there  is  any 
change  in  the  length  of  the  water  column.  Break  the  tube  and, 
taking  a  piece  an  inch  shorter  than  the  length  of  the  measured  water 
column,  put  it  in  water  as  before.  Does  the  water  come  out  at 
the  upper  end  of  the  tube  ?  Explain. 

131.  Absorption.  —  Whenever  a  liquid  is  brought  in  con- 
tact with  a  porous  solid,  and  wets  it,  the  liquid  immediately 
begins  to  pass  into  the  pores  of  the  solid ;  this  process  is  called 


126 


LIQUIDS 


FIG.  109 


absorption.  Blotting  paper  absorbs  ink,  and  a  lamp  wick, 
oil.  When  once  absorbed,  the  liquids  cannot  be  entirely 
removed  by  pressure.  A  sponge  can  never  be  pressed  dry, 
but  becomes  dry  only  when  evaporation  takes  place.  It  is 
evident  that  absorption  is  a  capillary  phe- 
nomenon and  that  every  pore  in  a  porous 
substance  acts  as  a  capillary  tube. 

Demonstration.  —  Procure  a  small  porous  cup 
such  as  is  used  for  a  battery  cell,  and  fit  in  the 
open  end  a  rubber  stopper  with  one  hole.  In  the 
stopper  fit  one  end  of  a  glass  tube  T,  bent  as  in 
Fig.  109.  Pour  mercury  into  the  end  of  this 
tube  and  let  it  come  to  rest  at  A:  The  heights 
in  the  two  branches  can  be  made  the  same  by 
letting  a  little  air  out  of  the  cup.  Lower  the  cup 
into  a  beaker  of  water  and  observe  the  change  in 

the  level  at  A.      Explain  this  action.     Measure  this  pressure  by 

putting  a  scale  back  of  the  tube  at  A. 

132.  Diffusion  of  Liquids.  —  Demonstration.  —  Fill  a  small 
jar  three  fourths  full  of  water  colored  with  blue  litmus,  and  pour  a 
small  quantity  of  sulphuric  acid  carefully  into  the 
bottom  of  the  jar  through  a  thistle  tube.  The 
litmus  will  be  colored  red  wherever  the  acid  comes 
in  contact  with  it.  If  now  the  jar  is  kept  in  a  quiet 
place,  the  acid  will  pass  through  the  litmus  solu- 
tion, and  after  a  time  the  entire  contents  of  the 
jar  will  be  red.  The  rate  at  which  the  mixing 
takes  place  can  be  determined  by  fastening  a 
meter  stick  to  the  jar  in  a  vertical  position  and 
taking  readings  of  the  top  of  the  red  liquid  at  uni- 
form intervals.  It  is  interesting  to  observe  that 
the  plane  which  separates  the  two  liquids  is 
always  exactly  horizontal. 

This  gradual  molecular  mixing  of  two  liquids  in  contact 
with  each  other,  which  takes  place  even  against  the  force 


MOLECULAR  FORCES  IN  LIQUIDS  127 

of  gravity,  is  called  diffusion.  Any  liquids  capable  of  mix- 
ing will  diffuse,  though  at  different  rates. 

Diffusion  is  a  proof  of  molecular  movements  in  liquids. 
It  is  the  vibration  of  the  molecules  of  sulphuric  acid  that 
forces  them  upward  through  the  water,  which  is  lighter 
than  the  acid.  If  the  temperature  is  raised,  the  vibration 
is  increased,  and  diffusion  takes  place  more  rapidly. 

133.  Osmose  ;  Osmotic  Pressure.  —  When  two  liquids  are 
separated  by  a  porous  membrane,  each  may  pass  through 
the  membrane  into  the  other  with 
more  or  less  freedom.  This  process 
is  called  osmose. 

Demonstration.  —  Tie  a  piece  of 
parchment  paper  over  the  end  of  a 
thistle  tube  and  fill  the  tubs  part  way 
up  the  stem  with  a  strong  solution 
of  copper  sulphate.  Thrust  it  into  a 
beaker  containing  water,  and  fix  it  in 
such  a  position  that  the  liquids  stand 
at  the  same  height,  both  inside  and 
outside  the  tube.  Set  the  beaker 
aside  for  some  time.  It  will  soon  be 
seen  that  the  height  of  the  liquid 
within  the  tube  is  increasing,  and  if 
the  experiment  is  carried  on  for  some 

time,  the  water  in  the  beaker  outside  the  tube  will  become  colored 
with  the  copper  sulphate  solution.  This  indicates  that  molecules 
have  passed  through  the  parchment  in  both  directions,  but  more 
rapidly  from  the  pure  water  than  from  the  solution. 

If  in  the  preceding  demonstration  the  upper  end  of  the 
thistle  tube  is  closed,  there  will  be  produced  an  osmotic 
pressure  on  the  inside  of  the  tube.  This  occurs  because 
water  molecules  pass  through  the  membrane  more  readily 


128  LIQUIDS 

than  do  copper  sulphate  molecules.  Since  copper  sulphate 
molecules  occupy  part  of  the  space  inside,  more  water  mole- 
cules, which  are  in  a  state  of  constant  vibration,  strike  the 
membrane  from  the  outside  than  from  the  inside,  and  for  this 
reason  more  of  them  pass  into  the  tube  than  out  of  it. 

High  osmotic  pressures  have  been  produced  by  the  use  of  a  semi- 
permeable  membrane  made  by  depositing  a  thin  surface  of  copper 
ferrocyanide  within  the  walls  of  a  porous  cup.  The  simplest  method 
of  doing  this  is  to  place  the  cup  in  a  solution  of  copper  sulphate  and 
then  fill  it  with  a  solution  of  potassium  ferrocyanide.  The  two  sub- 
stances enter  the  cup  from  opposite  sides  and  on  coming  in  contact 
form  a  semipermeable  membrane.  This  acts  as  a  molecule  sieve, 
allowing  the  water  molecules  to  pass,  but  not  those  of  a  solution. 
In  one  experiment  of  this  kind  a  solution  of  sugar  was  used,  and 
a  pressure  of  31  atmospheres  (about  465  Ib.  per  square  inch)  was 
obtained  in  one  hour  and  forty-five  minutes.  Before  another  read- 
ing could  be  taken,  the  pressure  became  so  great  as  to  shatter  the 
apparatus. 

Questions 

1.  Why  is  a  small  drop  of  mercury,  lying  on  a  table,  so  nearly 
spherical,  while  a  larger  drop  is  much  flattened  ? 

2.  If  two  straws  are  placed  on  the  surface  of  water  a  half  inch 
apart  and  then  a  drop  of  alcohol  is  placed  on  the  surface  between 
them,  they  will  immediately  separate.     Why? 

3.  Suppose  a  silk  thread  to  be  tied  loosely  to  two  sides  of  the 
frame  in  Fig.  103  and  the  film  broken  on  one  side  of  the  thread. 
What  form  will  the  thread  take? 

4.  Why  are  pictures  better  in  detail  when  printed  on  paper  with 
a  hard,  smooth  surface? 

6.  Why  is  it  so  hard  to  remove  the  stain  of  a  drop  of  kerosene 
from  marble  ? 

6.  Give  examples  of  useful  capillary  action. 

7.  Will  water  rise  or  fall  on  the  inside  of  an  oiled  glass  tube  ? 

8.  One  of  the  best  ways  to  make  a  glass  tube  closed  at  one  end  is 
to  break  the  tube  square  off  at  the  proper  length,  then  hold  that  end 


THE   MECHANICS  OF  LIQUIDS  129 

in  the  Bunsen  flame  so  that  it  will  be  uniformly  heated.  It  will 
then  soften,  the  opening  will  slowly  become  smaller,  and  finally  it 
will  make  a  smooth,  spherical  end.  Why? 

9.  A  thin  plate  of  glass,  a  lantern  slide  plate  for  example,  will 
float  when  tossed  on  the  surface  of  water.     Why  ? 

10.  A  piece  of  cloth,  the  corner  of  which  dips  in  a  dish  of  water, 
will  become  thoroughly  wet  in  a  short  time.  Explain. 

U.  Water  will  not  run  out  of  the  upper  end  of  a  capillary  tube, 
the  lower  end  of  which  dips  below  the  surface,  but  sap  runs  from  the 
end  of  a  maple  branch  that  has  been  cut  off.  Explain. 

12.  Could  a  lump  of  sugar  be  used  to  take  up  a  blot  of  ink  ? 

13.  A  glass  rod  is  sometimes  placed  against  the  edge  of  a  cup  in 
pouring  a  liquid  into  another  vessel.     Explain  its  action. 

14.  What  effect  does  keeping  the  surface  of  soil  well  cultivated 
have  upon  the  evaporation  of  water  from  the  surface? 

Problems 

1.  Water  rises  25  mm.  in  a  tube  of  a  certain  diameter.     What 
must  be  the  diameter  of  a  second  tube  in  which  it  will  rise  50  mm.  ? 

2.  If  a  liquid  will  rise  27  cm.  in  a  tube  .12  mm.  in  diameter, 
what  must  be  the  diameter  of  the  tube  for  it  to  rise  81  cm.  ? 

3.  How  high  must  a  stone  column  be  in  order  to  make  the  pres- 
sure at  the  base  equal  to  that  produced  by  the  osmotic  pressure 
of  a  sugar  solution,  i.e.,  465  Ib.  per  square  inch,  if  the  stone  weighs 
160  Ib.  per  cubic  foot? 


II.    THE  MECHANICS  OF  LIQUIDS 

134.  Transmission  of  Pressure  by  Liquids.  —  Whenever 
pressure  is  brought  to  bear  upon  a  solid,  the  molecules, 
being  unable  to  move  freely  over  one  another,  will  trans- 
mit the  pressure,  undiminished,  in  one  direction  only.  In 
the  case  of  liquids,  however,  the  free  movement  of  the  mole- 
cules over  one  another  secures  the  transmission  of  pressure, 
without  change,  in  all  directions. 

Rev. 


130  LIQUIDS 

Demonstration.  —  To  a  thin  glass  bottle  fit  a  straight  cork,  of 
such  a  size  as  to  go  into  the  neck  snugly.  Fill  the  bottle  with  water. 

Insert  the  cork  and  bring  pres- 
sure to  bear  upon  it  by  a  lever, 
as  in  Fig.  1 12.  The  shattering 
of  the  bottle  shows  that  the 
pressure  was  transmitted  in  all 
directions. 

The  action  of  the  mole- 
cules of  a  liquid  in  trans- 
mitting pressure  may  be 

illustrated  by  filling  a  bottle  with  peas  and  pressing  upon 
the  top  layers.  Since  each  pea  does  not  lie  directly  upon 
another,  but  in  a  depression  left  between  those  in  the  next 
lower  layer,  a  vertical  force  acting  upon  any  pea  will  be 
resolved  into  other  forces  in  the  direction  of  the  points  of 
contact  between  it  and  the  peas  which  it  touches. 

135.  Pascal's  Law.  —  Since  liquids  are  perfectly  elastic 
(i.e.,  have  no  elastic  limit)  under  compression,  and  since 
their   molecules   move   freely   over   one    another,    pressure 
brought  to  bear  upon  any  part  of  a  liquid  is  readily  carried 
to  any  other  part.     After  a  study  of  the  phenomena,  Pascal, 
a  French  scientist,  stated  this  law : 

Pressure  exerted  upon  any  part  of  an  inclosed  liquid  is 
transmitted  undiminished  in  all  directions.  This  pressure 
acts  with  equal  force  upon  all  equal  surfaces,  and  at  right  angles 
to  them. 

136.  The  Hydraulic  Press.  —  An  important  application 
of  the  principle  stated  in  Pascal's  Law  is  made  in  the  hydro- 
static or  hydraulic  press.     Figure  113  shows  a  simple  form 
in  section.     Two  pistons  or  plungers  A  and  B  pass  through 


THE  MECHANICS  OP  LIQUIDS 


131 


water-tight  collars  into  cylinders  C  and  D.    The  piston  A 

is  moved  by  the  lever  F  by  applying  the  power  at  P.     The 

body  K  to  be  compressed  is  placed  between  the  platform 

G    and    a    stationary 

framework    H  above 

it.     The  action  is  as 

follows  :    Both   cylin- 

ders and  the  connect- 

ing tube  E  being  full 

of  water,   the  piston 

A  is  forced  down,  the 

pressure  on  the  water 

C  closing  the  valve  d, 

and  forcing  the  valve 

v  open.      The    water 

displaced    by    A    is 

forced  through  E,  and 

passes  into  D,  where 

it  pushes  B  up,  and  compresses  K.     When  the  piston  A  is 

raised,   the  back  pressure  of  B  upon  the  water  closes  v, 

d  opens,   and   water  from  some  source   of  supply  passes 

through  it,  keeping  C  full.     The  next  stroke  simply  repeats 

the  action.     By  .  Pascal's  Law,  if  base  of  cylinder  B  is  20 

times  as  large  as  base  of  cylinder  A,  the  pressure  on  it 

will  be  20  times  as  great.     This  may  be  stated  as  follows  : 

The  pressure  applied  by  the   small   piston  :  The  pressure 

delivered  to  the  large  piston  =  The  area  of  the  small  piston  : 

The  area  of  the  large  piston, 


FIG.  113.  —  Hydraulic  press 


P:W  = 


=  d2  :  Z)2, 


d  and  D  being  the  respective  diameters  of  the  two  pistons. 
Since  Pascal's  Law  applies  to  all  liquids  and  since  oil  prevents 


132  LIQUIDS 

the  rusting  of  the  machine,  oil  is  frequently  used  instead  of 
water. 

The  fact  that  liquids  are  almost  incompressible  and  perfectly 
elastic  is  of  very  great  importance  in  connection  with  this  machine. 
A  pressure  of  100  Ib.  to  the  square  inch  compresses  water  only  .00033 
of  its  original  volume,  and  on  the  removal  of  the  pressure,  that 
volume  is  immediately  restored. 

The  hydraulic  press  is  largely  used  in  such  work  as  the  com- 
pression of  bales  of  cotton  and  other  bulky  materials  for  transporta- 
tion on  shipboard,  where  the  space  taken  by  a  package  of  freight 
is  a  determining  factor  in  the  expense  of  carrying  it. 

137.  Pressure  Due  to  Gravity.  —  The  principle  stated  in 
Pascal's  Law  holds  whether  the  force  employed  is  due  to 
the  pressure  of  weights  placed  on  a  piston  resting  upon  the 
surface  of  the  liquid,  or  to  the  pressure  of  an  added  layer  of 
water.     When  a  liquid  is  at  a  uniform  temperature  through- 
out, the  entire  mass  is  in  a  state  of  equilibrium,  and  there 
are  no  internal  currents,  as  can  be  seen  by  mixing  some 
heavy  sawdust  through  the  water.      This  means  that  the 
pressure  exerted  by  the  weight  of  a  liquid  at  any  point  in  the 
liquid  is  equal  in  all  directions. 

138.  Relation  of  Pressure  to  Depth.  —  Since  every  hori- 
zontal layer  of  a  liquid  has  to  support  the  weight  of  the 
liquid  above,  we  may  write  as  a  result  the  following  laws : 

I.  The  pressure  in  any  layer  is  proportional  to  its  depth. 

II.  The  pressure  is  the  same  at  all  points  in  the  same  hori- 
zontal layer. 

139.  Vertical  Downward  Pressure.  — When  a  liquid  is  con- 
tained in  a  vessel  with  vertical  sides,  the  weight  of  each  layer 
is  transmitted  undimimshed  to  the  layers  below.    Hence  each 
layer  bears  the  weight  of  the  liquid  above  it,  and  the  pressure 
on  the  bottom  will  be  the  weight  of  the  liquid  in  the  vessel. 


THE  MECHANICS  OF  LIQUIDS 


133 


Demonstration.  — 
Screw  one  of  the  glass 
vessels  shown  in  Fig.  114, 
into  the  ring  of  the  stand- 
ard.    By  fixing  the  index 
at  any  height  and  bring- 
ing   the    water    to    the 
height  indicated,  the  pressure  on 
the  flexible  base  will  be  shown 
by  the  position  of  the  pointer. 
On  lowering  the  water  supply, 
the  water  will  run  out  of  the 
glass  vessel.    Substitute  a  vessel 
of  another  shape.     When  the 
water    surface  is    raised  again 
to  the  fixed  index,  the  pointer 
will  read  the  same  as  before. 

The  above  demonstration  FIG.  114 

proves  that  the  pressure  on  the  bottom  of  a  vessel  containing 
a  liquid  is  entirely  independent  of  the  shape  of  the  vessel; 
with  a  given  liquid  it  depends  only  upon  the  depth  of  the  liquid 
and  the  area  of  the  base. 

Demonstration.  —  Use  salt  water,  which  is  heavier  than  fresh, 
and  it  will  be  found  to  require  less  height  for  the  same  pressure. 

From  this  we  see  that  the  pressure  on  the  bottom  of  a  vessel 
depends  also  upon  the  density  of  the  liquid. 

140.  Vertical  Upward  Pressure.  —  From  §  138  we  may 
infer  that  the  upward  pressure  at  any  point  below  the  surface 
of  a  liquid  is  equal  to  the  downward  pressure. 

Demonstrations.  —  Select  a  glass  tube,  like  a  lamp  chimney,  and 
a  glass  plate  or. disk  just  large  enough  to  cover  the  end  of  the  tube. 
Grind  the  end  of  this  tube,  and  the  glass  plate,  to  a  water-tight 
joint  with  emery.  Fasten  three  cords  to  the  plate  or  disk,  and  to  a 


134 


LIQUIDS 


FIG.  115 


single  cord,  as  in  Fig.  115.  Hold  the  disk  in 
place  over  the  bottom  of  the  tube  with  the  cord, 
and  push  the  tube  down  into  the  water  in  a  jar. 
The  upward  pressure  will  hold  the  disk  in  place 
without  the  cord.  Pour  water  into  the  tube  until 
the  disk  falls  off;  then  the  weight  of  the  water 
poured  in,  added  to  the  weight  of  the  disk,  will 
measure  the  upward  pressure. 

Place  in  the  bottom  of  a  shallow  pan  a  piece 
of  smooth  glass,  and  stand  upon  it  a  heavy  lamp 
chimney  of  the  form  shown  in  Fig.  116,  with  the 
lower  end  ground  smooth.  Pour  water  into  the 

chimney,  and  observe  that  when  it  rises  to  some  definite  noint,  A, 

it  will  not  rise  any  farther  because 

it  runs  out  at  the  bottom.     If  the 

chimney  is  held  down  by  placing 

a  finger  on  the  top  and  it  is  then 

filled  with  water,   it  will  remaiji 

full  as  long  as  it  is  held  down,  but 

when  the  finger   is   removed,  the 

water  suddenly   drops  to  A  and 

stops  there.     What  is  the  effect  of 

the  upward  pressure  of  the  water 

on  the  collar  of   the  chimney  in 

this  demonstration?  FIG.  116 

141.  Pressure  on  the  Side  of  a  Vessel.  —  When  a  liquid 
is  contained  in  a  vessel  with  vertical  sides,  the  pressure  at 
any  point  of  a  side  depends  upon  its  distance  from  the  sur- 
face of  the  liquid.  The  total  pressure  on  the  sides  of  the 
vessel  is  the  sum  of  all  these  pressures,  which  vary  from  zero 
at  the  surface  to.  a  maximum  at  the  bottom. 

The  pressure  of  a  liquid  upon  any  submerged  surface  is  equal 
to  the  weight  of  a  column  of  the  liquid  having  the  area  of  the 
surface  for  its  base,  and  the  depth  of  the  center  of  gravity  of 
the  given  surface  below  the  surface  of  the  liquid  for  ite  height. 


THE  MECHANICS  OF  LIQUIDS 


135 


NOTE.  —  See  §  83.  In  plane  surfaces  the  center  of  gravity  is  the 
center  of  area.  The  center  of  gravity  of  a  triangle,  for  instance,  is  a 
point  two  thirds  of  the  distance  from  any  angle  to  the  mid-point  of 
the  opposite  side. 

The  rule  just  given  (page  134)  applies  to  all  submerged 
surfaces,  whether  vertical,  horizontal,  inclined,  plane,  or 
curved.  If  the  surface  is  the  horizontal  base  of  the  vessel, 
the  height  of  the  column  will  be  the  total  depth  of  the  liquid. 

The  law  may  be  expressed  in  a  formula  as  follows  : 

Pressure  =  HaW,  (38) 

in  which  H  is  the 
height  of  the  surface 
of  the  liquid  above 
the  center  of  gravity 
of  the  submerged  sur- 
face, a  is  the  area 
of  the  submerged  sur- 
face, and  W  is  the 
weight  of  a  unit  vol- 
ume  of  the  liquid. 

A  cubic  foot  of  water  weighs  about  62.5  lb.,  or  1000  oz. 

Example.  —  The  pressure  of  water  on  any  submerged  body,  as 
in  Fig.  117,  is  found  as  follows  : 

Pressure  on  top  (HaW)  =  2  X  (2  X  3)  X  62.5  =    750  lb. 
Pressure  on  bottom         =  3  X  (2  X  3)  X  62.5  =  1125  lb. 
Pressure  on  ends  =  2  X  2.5  X  (2  X  1)  X  62.5  =    625  lb. 
Pressure  on  sides  =  2  X  2.5  X  (3  X  1)  X  62.5  =    937.5  lb. 
Total  pressure  =  3437.5  lb. 

142.  Center  of  Pressure.  —  The  center  of  pressure  on  a 
submerged  surface  is  the  point  of  application  of  the  resultant 
of  all  the  forces  acting  upon  it,  due  to  the  pressure  of  the 
liquid.  If  we  have  a  rectangular  side  to  a  vessel  containing 
water,  since  the  pressure  increases  from  the  top  to  the  bottom, 


117 


136  LIQUIDS 

it  is  evident  that  this  point  must  be  below  the  middle  of  the 
side.  Calculation  and  experiment  show  that  it  is  two  thirds 
of  the  distance  from  top  to  bottom. 

A  convenient  way  to  determine  the  position  of  this  point  is  as 
follows.     Lay  off  a  line  CB  (Fig.  118)  perpendicular  to  the  side  AB 
A  to  represent  the  pressure  at 

B.  Draw  the  line  CA.  Any 
lines,  as  ED  and  GF,  drawn 
perpendicular  to  AB,  will  rep- 
resent the  pressure  at  the 
points  D  and  F  respectively. 

E/     :     p why? 

7       1  The   area   of   the   triangle 

/    L ABC  will  represent  the  entire 


C1  K  B 

FlG    118  pressure  upon    AB,   and   the 

center  of  pressure  will  be  at 

the  point  H  where  the  perpendicular  from  the  center  of  area  of 
the  triangle  meets  the  side  A  B.  It  is  evident  that  this  point  will 
be  in  such  a  position  that  AH  =  f  AB,  since  the  center  of  gravity 
of  ABC  is  at  0,  a  point  such  that  AO  =  f  A  K. 

If  the  side  A  B  is  movable,  a  support  at  H  will  prevent  either  the 
top  or'  the  bottom  from  being  pushed  out. 

143.  The  Submarine.  —  To  be  able  to  travel  under  the 
surface  of  the  water  as  well  as  upon  the  surface,  a  boat  must 
be  so  designed  that  it  can  be  submerged  at  will,  shall  be 
water-tight  while  submerged,  can  be  propelled  while  sub- 
merged, and  can  be  brought  again  to  the  surface  when  desired. 

To  increase  the  weight  of  the  boat  so  that  it  will  submerge, 
water  is  let  into  tanks  provided  for  the  purpose.  To  bring 
the  boat  to  the  surface,  the  water  is  forced  out  of  the  tanks. 
Storage  batteries  (§  425)  supply  the  energy  for  driving  the 
electric  motors  that  run  the  propeller  while  the  boat  is  sub- 
merged. Figure  119  shows  the  exterior  of  a  modern  sub- 
marine^  and  Fig.  120  gives  a  view  of  the  compact  interior, 


THE   MECHANICS   OF   LIQUIDS 


137 


tist 


FIG.  119.  —  Submarine  as  Seen  on  the  Surface  of  the  Water 


FIG.  120.  —  Interior  of  a  Submarine  ;  the  Torpedo  Compartment 


138 


LIQUIDS 


FIG.  121 


To  permit  of  an  outlook  over  the  surface  of  the  water 
when  the  boat  is  submerged,  it  is  provided  with  a  peri- 
scope. This  consists  of  an 
upright  vertical  tube  leading 
from  the  interior  and  ending  in 
a  short  horizontal  piece  with  a 
lens  at  the  end.  There  is  a 
mirror  at  the  elbow  of  the 
tube  and  another  at  the  lower 
end  that  throws  the  image  sent 
by  the  lens  into  the  eyepiece. 
Figure  121  shows  a  periscope 
view  looking  76^  degrees  east 
of  north. 

144.  The  Surface  of  a  Liquid  at  Rest.  —  We  have  already 
seen  that  when  the  resultant  of  all  the  forces  that  act  upon 
any  point  in  a  liquid  is  zero, 
there  will  be  a  condition  of 
equilibrium,  and  the  liquid 
will  be  at  rest  .(§  137). 

In  order  that  the  surface 
of  a  liquid  may  be  at  rest,  it 
must  be  horizontal.  Sup- 
pose that  the  surface  is  not 
horizontal,  as  in  Fig.  122. 
The  force  of  gravity,  AB,  which  acts  upon  any  molecule 
upon  the  surface,  as  A,  may  be  resolved  into  two  forces, 
one  of  which,  AC,  is  perpendicular,  and  the  other,  AD, 
parallel  to  the  surface.  Now  the  first,  AC,  will  be  opposed 
by  the  resistance  of  the  liquid,  while  the  other,  AD,  will 
move  the  molecule  to  a  lower  level.  When  the  surface  is 
horizontal,  the  action  of  gravity  is  perpendicular  to  it, 


FK 


THE  MECHANICS  OF  LIQUIDS 


139 


and  if  we  try  to  resolve  this  force  into  two  components 
as  before,  we  find  that  the  component  perpendicular  to  the 
surface  is  equal  to  the  force,  and  the  horizontal  com- 
ponent is  zero.  Hence  no  movement  will  take  place,  and 
the  liquid  will  remain  at  rest. 

145.  Equilibrium  in  Com- 
municating Vessels.  —  When- 
ever a  number  of  vessels  are 
connected,  and  water  is  poured 
into  one  of  them,  it  will,  when 
it  comes  to  rest,  stand  at  the 
same  level  in  all.  This  is  in 
direct  accordance  with  the 
transfer  of  liquid  pressure  stated  in  Pascal's  Law. 
size,  nor  shape,  nor  position  affects  the  result. 


FIG.  123 


Neither 
It  is  in 


accordance  with  this  principle  that  water  "seeks  its  own 
level,"  that  fountains  play,  and  that  water  is  distributed  in 
city  waterworks. 

146.  The  Hydraulic  Ram  is  used  for  the  purpose  of  raising 
water  to  a  greater  height  than  its  source.     The  machine 

shown  in  Fig.  124 
uses  the  water  from 
a  stream  or  lake  to 
force  pure  spring 
water  into  an  ele- 
vated tank.  A  is 
the  drive  pipe  con- 
nected with  the 
water  supply,  a  few 
feet  above  the  ram. 
I  is  the  pure  water 


FIG.  124 


140 


LIQUIDS 


pipe,  and  P  is  the  service  pipe  which  carries  the  water  to 
the  tank.  The  water  flows  in  through  pipes  A  and  /,  and 
out  through  the  valve  B,  until  the  pressure  due  to  the 
increasing  velocity  is  enough  to  close  B.  When  this  valve 
closes,  the  momentum  of  the  moving  water  produces  what 
is  called  the  "  ramming  stroke/'  which  opens  the  valve  C, 
and  forces  water  into  the  air  chamber  D  until  the  pressure 
of  the  air  in  P  is  equal  to  the  pressure  of  the  water  in  A. 
When  this  occurs,  the  flow  through  C  is  reversed,  the  valve 
closes,  and  the  operation  is  then  repeated. 

A  proper  adjustment  of  the  quantities  of  water  in  A  and  7  re- 
spectively must  be  made  so  as  to  insure  that  only  pure  water  can  flow 
into  D.  If  the  water  coming  down  A  is  pure  enough  to  be  sent 

into  the  tank,  I  is  removed,  and  H  is  closed 

with  a  screw  plug. 

147.  The  Turbine  Water  Wheel  is 
another,  more  important,  machine  for 
utilizing  the  pressure  of  a  column  of 
water.  The  well-known  form  of  lawn 
sprinkler  which  throws  water  in  small 
streams  from  holes  in  one  side  of  each  of 
four  revolving  arms,  is  a  simple  reaction 
turbine.  The  rotation  is  produced  by 
the  reaction  of  the  air  and  the  difference 
in  pressure  on  the  opposite  sides  of  the 
tube.  A  jet  of  water  directed  against 
the  paddles  of  a  paddle  wheel  so  as  to 
make  it  rotate  by  the  force  of  the  impact 
would  illustrate  the  principle  of  an  im- 
pulse turbine.  Both  principles  are  used 
in  turbine  water  wheels,  which  are  made 

FIG.  125.  — A  Turbine     . 

at  Niagara  Falls          in  VariOUS 


U  Water 


THE   MECHANICS   OF   LIQUIDS  .        141 

At  Niagara  Falls  water  goes  from  the  vertical  penstock 
into  the  central  part  of  a  horizontal  wheel  and  passes  outward 
between  fixed  guides,  G,  Fig.  126, 
which  direct  it  against  the  vanes  V 
attached  to  the  rotating  part  of  the 
wheel.  The  motion  may  be  pro- 
duced either  by  the  impact  upon  V 
in  the  direction  of  the  heavy  arrow, 
or  by  the  reaction  as  the  water  leaves 
the  wheel  in  the  opposite  direction. 

The  wheel  rotates   a  vertical   shaft   connected   with   the 
dynamo  at  the  top  of  the  wheel  pit  (Fig.  125). 

In  another  type  of  turbine,  the  water  enters  the  outer  part  of  the 
wheel  through  fixed  guides,  and  leaves  the  inner  part  through  mov- 
ing vanes. 

Questions 

1.  Why   do    liquids    exert    pressure    on    submerged   surfaces? 
What  governs  the  amount  of  this  pressure? 

2.  State  the  rule  for  finding  the   pressure  on  any  submerged 
surface. 

3.  State  Pascal's  Law. 

4.  Name  the  essential  parts  of  a  hydraulic  press. 

6.  State  the  Jaw  of  the  hydraulic  press.  Can  oil  be  used  to 
operate  it  as  well  as  water  ? 

6.  If  the  areas  of  the  large  and  small  pistons  of  a  hydraulic 
press  are  to  each  other  as  20  is  to  2,  how  would  the  total  pressures 
exerted  on  each  compare?     How  would  the  pressures  per  square 
inch  on  each  compare?    How  would  the  distances  moved  through 
by  each  compare? 

7.  Why  would  not  air  answer  so  well  as  water  in  a  hydraulic  press? 

8.  Why  is  a  dam  built  with  the  base  thicker  than  the  top  ?     Why 
is  the  upper  face  usually  made  slanting  up  stream  ? 

9.  What  determines  the  pressure  at  the  nozzle  of  a  fire  hose 
when  it  is  connected  directly  to  the  hydrant? 


142 


THE    MECHANICS    OF   LIQUIDS  143 

10.  If  oil  and  water  are  shaken  together  in  a  test  tube  and  it  is 
then  set  aside,  what  will  happen?     Why? 

11.  Why  is  an  air  chamber  used  in  a  hydraulic  ram? 

12.  What  is  the  direction  of  the  pressure  of  water  on  the  walls 
of  the  vessel  that  contains  it? 

13.  A  hole  2  ft.  long  and  1  ft.  wide  is  broken  in  the  side  of  a  ship. 
What  would  be  the  result  of  weighting  a  piece  of  heavy  sail  cloth 
with  a  piece  of  iron  at  each  of  the  two  corners  and  letting  it  down  the 
side  of  the  ship  over  the  hole? 

Problems 

1.  The  area  of  the  large  piston  of  a  hydraulic  press  is  300  sq.  in., 
that  of  the  small  piston  is  12.5  sq.  in.     What  pressure  is  delivered 
by  the  large  piston  when  a  force  of  580  Ib.  is  applied  to  the  small 
piston? 

2.  What  must  be  the  area  of  the  large  piston  of  a  hydraulic  press 
in  order  that  a  force  of  178  Ib.  applied  to  the  small  piston,  the  area 
of  which  is  0.48  sq.  in.,  will  raise  a  load  of  2000  Ib.? 

3.  The  small  plunger  of  the  hydraulic  press  shown  in  Fig.  113 
is  2  in.  in  diameter  and  the  large  plunger  is  14  in.  in  diameter.    What 
upward  pressure  on  B  will  a  power  of  30  Ib.  exert  if  the  lever  is  3  ft. 
long  and  the  distance  from  the  plunger  to  the  fulcrum  is  5  in.? 

4.  The  diameter  of  the  large  cylinder  of  a  hydraulic  press  is  ,30 
in.,  that  of  the  small  cylinder  1  in.    What  is  the  pressure  exerted  by 
the  large  piston  when  a  force  of  100  Ib.  is  applied  to  the  small  piston? 

6.  The  pistons  of  a  hydraulic  press  are  respectively  ^  In.  and  24 
in.  in  diameter.  What  pressure  must  be  used  on  the  small  piston 
to  produce  a  pressure  of  40,000  Ib.  on  the  large  piston? 

6.  Find  the  pressure  on  the  bottom  of  a  tank  18  ft.  long  and  7 
ft.  wide  when  filled  with  water  to  a  depth  of  4.5  ft. 

7.  What  is  the  pressure  on  the  bottom  of  a  tank  8  cm.  long, 
5  cm.  wide,  and  4  cm.  deep  when  filled  with  water?     When  filled 
with  mercury,  the  weight  of  which  is  13.6  g.  per  c.c.? 

8.  What  is  the  pressure  against  one  end  of  a  swimming  pool  60 
ft.  long,  25  ft.  wide,  and  9  ft.  deep?    What  would  the  pressure  be  if 
the  length  were  only  40  ft.? 

9.  What  is  the  pressure  in  pounds  per  square  inch  in  a  water 
pipe  230  ft.  below  the  surface  of  the  water  in  the  reservoir? 


144 


LIQUIDS 


FIG.  128 


10.  The  steel  water  tank  shown  in  Fig.  128 
has  an  internal  diameter  of  22  ft.     The  height 
of  the  cylindrical  portion  is  28  ft.,  and  the  bot- 
tom is  a  hemisphere.     When  the  tank  is  full,  the 
water  surface  is  100  ft.  above  the  ground.     How 
many  gallons  does  the  tank  hold?1     What  is  the 
vertical  pressure  on  the  bottom?     What  is  the 
pressure  on  the  cylindrical  side?     What  is  the 
pressure  per  square  foot  at  the  bottom  of  the 
feed  pipe? 

11.  An  hydraulic  elevator  with  a  plunger  8 
in.  in  diameter  is  connected  with  water  works 
having  a  head  of  186  ft.     What  is  the  lifting 
power  of  the  water  upon  the  plunger  in  the  ele- 
vator well?     If  the  elevator,  with  plunger,  weighs 
1700  Ib.    more    than    its    counter-weight,    how 
many  people  averaging  150  Ib.  each,  can  it  carry? 

12.  At  the  depth  of  100  ft.,  what  is  the  pressure  on  each  square 
foot  of  the  surface  of  a  submarine,  sea  water  being  1.025  times  as 
heavy  as  fresh  water? 

13.  Find  the  pressure  in  grams  against  a  stopper  5  sq.   cm. 
in  area  placed  in  a  hole  in  the  side  of  a  tank    of  mercury  with 
its  center  35  cm.   below  the  surface. 

14.  The  two  leaves  of  a  lock 
gate  are  each  12  ft.  long  and 
15   ft.    high.      What    is    the 
pressure    on    each   when    the 
lock  is  filled  with  fresh  water? 

15.  What    is    the    pressure 
per  square  inch  of  the  water 
striking  the  blades  of  a  tur- 
bine water  wheel  when  the 
head  of  water  is  48  ft.? 

16.  Where  is  the  center  of 

pressure  on  a  dam  24  ft.  long  and  12  ft.  high? 


FIG.  129.  —  Lock  Gate 


Vol.  of  cylinder  =  TT  r2  X  H.  Vol.  of  sphere  =  f  TT  r3.  1  gal.  =  231  cu.  in. 


Rev. 


145 


146 


LIQUIDS 


17.  Where  is  the  center  of  pressure  on  the  leaves  of  the  lock  gate 
mentioned  in  problem  14? 

18.  A  box  1  m.   long,  80  cm.  wide,  and  60  cm.  deep  is  filled 
with  water.    Find  the  pressure  on  the  bottom,  sides,  and  ends  in 
kilograms. 

19.  An  air-tight  wooden  box  60  cm.  long,  50  cm.  wide,  and 40  cm. 
deep  is  weighted  so  that  it  sinks  to  the  bottom  of  a  pond  6  m. 
deep.     Compute  the  pressure  with  which  the  water  tends  to  crusli 
the  box. 


III.    SPECIFIC   GRAVITY 

148.  The  Principle  of  Archimedes.—  Demonstrations.  —Tie 

a  strong  thread  to  a  stone,  suspend  the  stone  from  a  spring  scale,  and 

note  its  weight.  Weigh  again, 
letting  the  stone  hang  in  a 
beaker  of  water,  and  the  scale 
will  be  found  to  read  less. 
Why? 

Suspend  from  one  side  of 
a  balance  a  short  brass  tube 
A  (Fig.  131),  and  from  a  hook 
in  the  closed  bottom  of  this 
tube  suspend  a  solid  cylinder 
B,  which  will  just  fill  the  tube. 
Put  weights  upon  the  other 

scale  pan  until  the  beam  is  horizontal.     Immerse  B  in  water,  and 

the  equilibrium  will  be  destroyed.     Fill  A  with  water,  and  the 

equilibrium  will  be  restored. 

We  learn  from  the  above,  both  that  a  body  appears  to 
lose  weight  when  it  is  immersed  in  a  liquid,  and  that  the 
amount  of  this  apparent  loss  is  exactly  the  weight  of  the  water 
displaced.  The  fact  that  a  submerged  body  seems  to  weigh 
less  in  a  liquid  than  in  the  air  was  observed  by  the  Greek 
philosopher  Archimedes  in  the  third  century  B.C.  He  not 
only  observed  the  apparent  loss  of  weight,  but  discovered  the 


FIG.  131 


SPECIFIC  GRAVITY 


147 


exact  law  governing  it,  hence  the  law  is  called  the  Principle 
of  Archimedes.     It  may  be  stated  as  follows : 

A  body  immersed  in  a  liquid  is  buoyed  up  by  a  force  equal 
to  the  weight  of  the  displaced  liquid. 

This  tendency  of  a  liquid  to  lift  a  submerged  body  is  called 
its  buoyancy,  and  depends  in  amount  upon  the  density  of  the 
liquid  and  the  size  of  the  body. 

Since  weight  is  the  measure  of  the  mutual  attraction  be- 
tween the  earth  and  the  body  weighed,  there  can  be  no 
real  loss  of  weight,  when  a  body  is  submerged  in  water.  If, 
however,  we  suspend  the  body  by  means  of  a  spring  scale 
and  weigh  it  in  the  air  and  then  weigh  it  again  in  water,  there 
will  be  a  decrease  indicated  on  the  scale,  and  it  is  this  decrease 
that  is  often  called  loss  of  weight. 

If  a  body,  a  cube  for  instance,  is  immersed  in  a  liquid,  the 
horizontal  pressure  acting  upon  any  side  will  be  exactly 
counterbalanced  by  the  pressure  upon 
the  opposite  side.  The  downward 
pressure  upon  the  upper  surface  A 
will  be  equal  to  the  weight  of  a  col- 
umn of  water  having  for  its  base  the 
area  of  A,  and  for  its  height  the  depth 
of  A  below  the  surface  of  the  water. 
The  upward  pressure  upon  the  lower 
surface  B  will  be  equal  to  the  weight 
of  a  column  of  water  having  for  its 
base  the  area  of  B,  and  for  its  height 
the  depth  of  B  below  the  surface  of 
the  water.  The  difference  between 
these  pressures  is  the  buoyancy  of  the  liquid,  and  is  equal 
to  the  weight  of  a  quantity  of  the  liquid  that  has  the  same 


FIG.  132 


148  LIQUIDS 

volume  as  the  submerged  cube.     This  conclusion  is  verified 
by  the  result  of  experiment. 

149.  Floating  Bodies.  —  When   a   body  is   placed   in   a 
liquid,  the  position  it  finally  takes  will  depend  upon  the 
relative  densities  of  the  body  and  the  liquid.     If  a  stone 
or  a  drop  of  mercury  is  placed  in  water,  it  will  sink,  since 
it  is  heavier  than  the  water.     If  a  drop  of  olive  oil  is  placed 

in  a  mixture  of  alcohol  and  water,  of  the 
same  density  as  itself,  it  will  remain  wherever 
it  is  placed.  If  a  piece  of  wood  is  placed  in 
water,  it  will  rise  to  the  surface  and  float.  The 
Principle  of  Archimedes  applies  to  each  of 
these  cases,  however,  and  we  may  write  this 
Law  of  Floating  Bodies  : 

A  floating  body  displaces  a  volume  of  liquid 
that  has  the  same  weight  as  the  floating  body. 

Demonstration.  —  Make  a  bar   of    pine  wood 
25  cm.  long  and  1  cm.  square.     Bore  a  hole  in  one 
end  and  run  in  molten  lead.     Divide  off  one  side 
of  the  bar  into  centimeters.     Cover  the  bar  with 
melted  paraffin,  melting  it  into  the  pores  of  the 
FIG  133        wood  over  a  flame.     Float  the  bar  upright  in  a  tall 
jar  of  pure  water  (Fig.  133) ;  then,  since  1  cc.  of 
water  weighs  1  g.,  the  reading  of  the  height  at  which  it  floats  will 
give  the  approximate  weight  of  the  bar  in  grams. 

150.  Density.  —  The  quantity  of  matter,  or  the  mass,  in 
a  unit  volume  measures  the  density  of  a  substance.     If  a 
piece  of  lead,  for  example,  has  a  mass  of  45.4  g.  and  a  volume 
of  4  cc.,  then  the  density  of  this  lead  equals  45.4  -r-  4  =  11.35 
g.  per  cubic  centimeter.    The  general  expression  is 

_       .  Mass 

Density  =  ==—. 

Volume 


SPECIFIC   GRAVITY  140 

Hence,  masses  of  equal  volumes  are  directly  proportional  to 
their  densities,  and  volumes  of  equal  masses  are  inversely  pro- 
portional to  their  densities. 

The  relative  density  of  a  substance  is  the  ratio  of  its  den- 
sity to  the  density  of  pure  water  at  a  temperature  of  4°  C.  If 
we  assume  the  quantity  of  matter  in  1  cc.  of  pure  water  at 
4°C.  as  a  unit  of  density,  the  density  of  the  water  will  be  1, 
and  the  quantity  of  matter  in  1  cc.  of  any  other  substance 
will  measure  its  relative  density. 

The  density  of  water  varies  with  its  temperature  as  well  as  with  its 
purity.  The  temperature  4°C.  is  taken  for  the  standard  density 
because  the  density  of  water  is  greatest  at  that  temperature.  In 
order  to  get  the  most  accurate  results  in  the  following  experiments, 
distilled  water  at  4°  C.  must  be  used. 

151.  Specific  Gravity.  —  Since  the  ratio  between  the 
weights  of  equal  volumes  of  substances  in  the  same  place  is 
the  same  as  the  ratio  of  their  masses,  we  can  use  the  term 
specific  gravity  in  place  of  relative  density.  Since,  also,  pure 
water  is  taken  as  the  standard  in  specific  gravity,  we  may 
express  it  by  the  following  formula  : 

~  Weight  of  the  body  in  air 

Weight  of  an  equal  volume  of  water' 
Q  Weight  of  the  body  in  air 

Buoyant  force  of  water  displaced' 


In  this  expression  W  is  the  weight  of  the  body  in  air,  and 
Wf  its  apparent  weight  in  water. 

Since  there  are  different  systems  of  weights  and  meas- 
ures it  is  evident  that  the  number  representing  the  density 
of  a  substance  will  depend  upon  the  system  of  units  used, 
while  its  relative  density  or  its  specific  gravity  will  be  the 


150 


LIQUIDS 


same  in  all  systems.  For  example,  the  density  of  wrought 
iron  in  the  C.  G.  S.  system  is  7.85,  which  means  that  it  has 
a  mass  of  7.85  g.  per  c.  c.  In  the  F.  P.  S.  system  its  density 
is  489,  which  means  that  its  mass  is  489  Ib.  per  cubic  foot. 
In  both  systems  its  specific  gravity  is  7.85,  which  means  that 
its  weight  is  7.85  times  that  of  an  equal  volume  of  water. 

The  density  of  a  substance  depends  upon  its  physical 
condition.  If  the  substance  is  a  mineral,  its  density  de- 
pends upon  its  purity.  If  the  substance  is  a  metal,  its  density 
is  affected  by  the  treatment  received  in  the  process  of  manu- 
facture ;  for  instance,  whether  it  is  cast,  or  drawn  into  wire. 
The  density  of  an  alloy  depends  upon  the  proportional  parts 
of  the  metals  composing  it. 

The  accompanying  table  of  densities  and  specific  gravities  is  made 
by  taking  the  average  of  results  found  by  different  observers.  With 


DENSITY 
in  g.  per  c.c. 
-  SP.  GR. 

DENSITY 
in  Ib.  per 
cu.  ft. 

gf'g 

OD     O 

fc  acu 
0*1 

S&4* 
g£d 

Q.S° 

Charcoal  (oak)    . 

0.57 

35. 

.Iron  (gray  cast) 

7.08 

442 

Butter   .... 

0.86 

53. 

Zinc  (cast)     .     . 

7.10 

443 

Paraffin      .     .     . 

.0.89 

55.5 

Tin  (cast)      .     . 

7.29 

455 

Ice    

0.917 

57.3 

Iron  (wrought)  . 

7.85 

489 

Beeswax     .     .     . 

0.96 

60. 

Brass  (yellow)    . 

8.44 

527 

Sandstone  .     .     . 

2.35 

.146.5 

Brass  (red)    .     . 

8.60 

536 

Feldspar     .     .    ,. 

2.55 

160. 

Nickel.    .     .     . 

8.60 

536 

Aluminum  (cast) 

2.57 

160.5 

Copper  (cast)     . 

8.88 

553 

Glass  (common)  . 

2.60 

162.5 

Silver  (cast)  .     . 

10.45 

652 

Quartz 

2.65 

165 

Lead  (cast)    . 

11.34 

708 

Marble  .... 

2.65 

165. 

Mercury  .     .     . 

13.596 

848 

Granite  .... 

2.75 

171. 

Gold  (cast)    .     . 

19.30 

1205 

Garnet  .     ...     . 

3.70 

232. 

Platinum  .     .     . 

21.45 

1338 

SPECIFIC  GRAVITY 


151 


slight  exception  they  are  as  reported  in  the  Physical  Tables  pub- 
lished by  the  Smithsonian  Institution. 

152.  To  find  the  Specific  Gravity  of  a  Body  Heavier  than 
Water.  —  Tie  a  light  cord  about  the  body,  suspend  it  from 
one  arm  of  a  balance,  and 
weigh  it ;  call  this  weight 
W.  '  Weigh  again  with  the 
body  suspended  in  water, 
as  in  Fig.  134.  Call 
this  apparent  weight  W . 
Substitute  these  values  in 
Formula  39,  and  the  result 
will  be  the  specific  gravity 
of  the  body.  FlG- 134 

EXAMPLE.  — The  weight  of  a  stone  in  air  (W)  =  146  g. 
Its  apparent  weight  in  water  (W'}  =    94  g. 

Since  the  specific  gravity  is  the  weight  of  the  stone  divided 
by  the  weight  of  an  equal  volume  of  water  and  since  the 
difference  between  the  weight  of  the  stone  in  air  and  in 
water  is  the  buoyant  force  of  the  water,  or  the  weight  of  a 
volume  of  water  equal  to  that  of  the  stone : 


Sp.  gr. 


146 


146  -  94 


146 
52 


153.  To  find  the  Specific  Gravity  of  a  Body  Lighter  than 
Water.  —  Since  the  buoyant  force  of  the  water  is  greater  than 
the  weight  of  the  body,  it  will  float,  and  it  must  be  fastened  to 
a  heavy  body  in  order  to  submerge  it.  The  specific  gravity 
can  be  found  as  follows  : 

Weigh  the  body  in  air  (W),  then  weigh  a  heavy  sinker 
in  water  and  call  its  apparent  weight  S.  Tie  the  sinker 


152  LIQUIDS 

to  the  body  and  weigh  them  both  in  water.     Call  the  appar- 
ent weight  W".     Compute  the  specific  gravity  from  the  form- 

W 

ula  Sp.  gr.  =  ^        ^  _  w    . 

EXAMPLE.  —  Suppose  a  piece  of  wood  weighs  40  g.  in  air  (W}, 
a  sinker  registers  50  g.  in  water  (S),  and  the  two  when  tied  together 
and  submerged  register  30  g.  (W"}.  It  is  evident  that  the  wood 
not  only  displaces  its  own  weight  of  water,  but  buoys  up  20  g.  of  the 
weight  of  the  sinker ;  therefore  the  wood  displaces  40  +  20  g.  of 

40  40 

water,  hence  its  specific  gravity  is  A~    ,    /-n orTT  =  ^  =  •*•• 

"xU   ~p  \O\J  —  OU^  o(J 

154.  To  find  the  Specific  Gravity  of  Liquids.  —  (a)  By  the 

Specific  Gravity   Bottle.  —  Any   bottle   with   a   small   neck 

having  a  fixed  mark  around  the  neck  can  be  used  in  this 

method.     Weigh  the  bottle  when    empty   (a).     Fill  with 

water  to  the  fixed  mark  and  weigh  (6).     The  difference  gives 

the  weight  of  water  (b  —  a).     Fill  with  the  required  liquid 

and  weigh  (c).     The  difference  (c  —  a)  gives  the  weight  of 

the  same  volume  of  the  liquid.     Then  the  specific  gravity 

.,,  ,  Weight  of  liquid  _  c  —  a 

Weight  of  equal  volume  of  water       b  —  a 

EXAMPLE.  —  Weight  of  the  empty  bottle  (a)  =  54  g. 
Weight  of  the  bottle  filled  with  water  (6)  =  304  g. 
Weight  of  the  bottle  filled  with  the  liquid  (c)  =  252.25  g. 

.  c  -  o       252.25  -  54      198.25 
"  b  -  a  ~"    304  -  54  250 

Specific  gravity  bottles  are  usually  made  to  hold  a  certain 
number  of  grams  of  water  at  a  stated  temperature,  and  are 
so  marked. 

If  the  bottle  holds  1000  g.  of  water,  the  specific  gravity 
can  be  obtained  directly.  For  example,  if  a  thousand-gram 


SPECIFIC  GRAVITY 


153 


bottle  holds  1240  g.  of  hydrochloric  acid,  then  the  specific 

gravity  of  the  acid  is  1.240. 

(6)    By  the  Method  of  Balancing  Columns.  —  A  good  form 

of  apparatus  for  this  method  is  that  of  Hare,  shown  in  Fig.  135. 

A  and  B  are    glass  tubes  joined  at  the 

upper  ends  to  the  branches  of  a  Y  tube. 

The.  other  end  of  the  Y  is  joined  to  a 

rubber  tube  R.     The  lower  end  of  each 

tube  dips  into  a  liquid  in  a  beaker.    C  is  a 

clamp  and  M  a  meter  stick.     When  pres- 
sure is  reduced  in  R  the  liquids  rise  to 

heights    that   are    inversely   proportional 

to  their  specific  gravities.     If  water  is  in 

A  and  alcohol  in  B,  the  specific  gravity 

of  the  alcohol  will  be  as  follows : 

0      ^          Height  of  A     .     1.1^         i 

Sp"  Gr"  ==  Height  of  B'  the  helghts  t0  be 
measured  from  the  surface  of 
the  liquid  in  each  case. 

(c)  By  the  Hydrometer.  —  A 
constant-weight  hydrometer 
usually  consists  of  a  small  glass 
tube  to  which  two  larger  bulbs 
are  sealed.  Either  mercury  or  small  shot  are  put 
into  the  lower  bulb  in  order  to  keep  the  stem  of 
the  instrument  vertical.  For  liquids  heavier  than 
water  the  unit  mark  is  placed  at  the  upper  end 
of  the  stem,  which  is  graduated  decimally.  This 
instrument  (Fig.  136)  is  used  by  floating  it  in 
the  liquid  in  a  hydrometer  jar,  and  reading  the 

height  to  which  the  liquid  stands  on  the  stem. 

Special  forms  of  hydrometers  are  used  for  special  liquids. 


FIG.  135 


FIG.  136 


154  LIQUIDS 

The  alcoholmeter  is  used  for  determining  the  percentage  of 
absolute  alcohol  in  spirits,  and  the  lactometer  for  testing  the 
purity  of  milk. 

Questions 

1.  Why  do  liquids  buoy  up  objects  immersed  in  them? 

2.  What  governs  the  amount  of  this  buoyant  effect? 

3.  Why  do  some  objects  float  on  water  while  others  sink? 

4.  State  the  law  governing  the  buoyant  effect  of  liquids  on 
bodies  immersed  in  them.     State  the  law  for  floating  bodies. 

5.  Why  is  not  a  submerged  body  pushed  sideways  by  the  pres- 
sure of  the  water  when  submerged  in  it? 

6.  Define  density;   specific  gravity. 

7.  What  is  taken  as  the  unit  in  specific  gravity  ? 
Why? 

8.  Suppose  you  weigh  a  glass  bulb  loaded  with 
mercury,  like  Fig.  137,  first  in  air,  then  in  water,  and 
then  in  kerosene.     How  would  you  find  the  specific 
gravity  of  the  kerosene  ? 

9.  Why  does  a  hydrometer  float  vertically  in  a 
FIG.  137         T      •  i  o  • 

liquid? 

10.  Where  is  the  unit  mark  placed  on  a  hydrometer  that  is  to  be 
used  for  liquids  lighter  than  water?     Why? 

Problems 

1.  A  boy  can  lift  100  Ib.     How  many  cubic  inches  of  granite, 
the  sp.  gr.  of  which  is  2.75,  can  he  lift?     How  many  cubic  inches  of 
granite  can  he  lift  in  water? 

2.  A  block  of  wood  1  ft.  square  and  2  ft.  long  is  pushed  down 
into  the  water  until  its  upper  side  is  6  in.  below  the  surface.     What 
is  the  upward  pressure  upon  the  bottom  of  the  block?     What  is 
the  downward  pressure  of  the  water  on  the  top  of  the  block  ?     How 
much  pressure  is  required  to  keep  the  block  in  place,  if  its  specific 
gravity  is  .65  ?    How  much  pressure  would  be  required  to  keep  it  at 
a  depth  of  2ft.? 

3.  An  automobile  weighing  3600  Ib.  is  ferried  across  a  river  on  a 
flatboat.     How  much  deeper  is  the  boat  in  the  water  after  the 


SPECIFIC  GRAVITY  155 

automobile  is  on  board  than  before,  if  the  boat  is  18  ft.  long  and 
10ft.  wide? 

4.  Ice  forms  16  in.  thick  over  the  surface  of  a  lake.     What  is  the 
weight  of  a  cake  2  ft.  long  and  18  in.  wide?    How  much  of  its  thick- 
ness will  be  above  the  water  when  it  floats  ? 

5.  An  iceberg  80  ft.  thick  cracks  off  from  a  glacier  and  floats 
away  into  the  sea.     How  high  does  it  stand  above  the  water  surface  ? 

6.  A  cake  of  ice  6  ft.  square  and  2  ft.  thick  is  floating  on  a  lake. 
How  much  will  it  settle  in  the  water  if  a  man  weighing  180  Ib. 
stands  upon  it  ? 

7.  A  river  scow  60  ft.  long,  22  ft.  wide,  and  5  ft.  out  of  water 
when  empty  is  loaded  with  coal  until  the  top  of  the  boat  is  within 
6  in.  of  the  surface.     How  many  tons  of  2240  Ib.  each  in  the  load? 

8.  A  block  of  sandstone  6  cm.  long,  4  cm.  wide,  and  2  cm.  thick 
weighs  112.8  g.     What  is  its  density  in  grams  per  cubic  centimeter? 

9.  A  block  of  nickel  weighs  86  g.  in  air  and  has  a  volume  of 
10  cc.     What  is  its  specific  gravity?    What  is  its  density? 

10.  A  piece  of  anthracite  coal  weighs  80  g.  in  water  and  has  a 
volume  of  120  c.c.   What  is  its  specific  gravity?     What  is  its  weight 
in  air? 

11.  The  metal  from  which  the  United  States  Standard  Meter  is 
made  is  90  %  platinum  and  10  %  iridium  and  weighs  1348  Ib.  per 
cubic  foot.     What  is  its  density  in  grams  per  cubic  centimeter? 

12.  An  ordinary  brick  is  8  in.  long,  4  in.  wide,  and  2  in.  thick 
and  weighs  5  Ib.    What  is  its  apparent  weight  when  submerged  in 
water? 

13.  A  boy  agreed  to  carry  a  gallon  (231  cu.  in.)  of  mercury  across 
the  room.     How  much  did  he  have  to  lift? 

14.  A  glass  stopper  weighs  162  g.  in  air  and  has  an  apparent 
weight  of  100  g.  in  water.     Find  its  specific  gravity  and  the  density 
of  glass  in  pounds  per  cubic  foot. 

16.  A  piece  of  sandstone  had  an  apparent  weight  of  168  Ib.  when 
submerged  in  water.  When  lifted  from  the  water  it  weighed  293 
Ib.  What  was  its  volume? 

16.  A  cast  iron  machine  frame  weighing  two  tons  fell  overboard 
in  a  canal.  How  great  a  pull  will  be  required  to  bring  it  from  the 
.bottom  to  the  surface  of  the  water?  How  much  greater  must  the 
pull  be  to  lift  it  in  the  air? 


156  LIQUIDS 

17.  A  block  of  metal,  having  a  volume  of  one  cubic  decimeter,  is 
suspended  from  the  hook  of  a  spring  balance  and  its  reading  noted. 
It  is  then  lowered  into  water  until  it  is  half  submerged.     What  is 
the  change  in  the  reading  of  the  balance? 

18.  A  piece  of  platinum  2  c.c.  in  volume  was  suspended  from  a 
spring  scale  and  its  weight  noted.     It  was  then  lowered  into  mercury. 
What  was  the  weight  of  the  platinum  in  air?    What  was  its  apparent 
weight  in  mercury? 

19.  A  piece  of  iron  bar  weighed  94  Ib.  in  air  and  82  Ib.  in  water. 
What  kind  of  iron  was  it  and  how  many  cubic  inches  did  it  contain? 

20.  A  block  of  wood  weighing  125  g.  in  air  was  tied  to  a  sinker 
which  weighed  100  g.  in  water.     On  being  weighed  together  in  water 
the  weight  was  63  g.     What  was  the  specific  gravity  of  the  wood? 

21.  A  bottle  weighing  236  g.  was  filled  with  water   and  then 
weighed  486  g.      On  being  filled  with  olive  oil  it  weighed  465  g. 
What  was  the  specific  gravity  of  the  oil? 

22.  A  bottle  with  stopper  and  pinchcock  weighs  350  g.     After 
most  of  the  air  in  it  has  been  pumped  out  it  weighs  348.341  g.     The 
pinchcock  is  then  opened  under  water,  and  when  water  has  taken 
the  place  of  the  air  removed  by  the  pump,  the  bottle  and  contents 
weigh  1631.591  g.     What  was  the  density  of  the  air? 

23.  A  column  of  water  in  one  branch  of  the  tube  shown  in  Fig. 
135  read  129  cm.  while  a  column  of  milk  in  the  other  branch  read 
125  cm.     What  was  the  specific  gravity  of  the  milk? 

24.  A  column  of  water  was  balanced  in  the  same  piece  of  apparatus 
by  a  column  of  turpentine.     The  water  stood  at  22  cm.  and  the 
turpentine -at  25  cm.      What  was  the  specific  gravity  of  the  turpen- 
tine?    What  was  its  density  per  cubic  foot? 

25.  A  cubic  foot  of  granite  weighed  171  Ib.  in  air.      It  was  then 
weighed  when  submerged  in  turpentine.     What  was  its  apparent 
weight? 


CHAPTER  V 


GASES 

155.  Gases  and  Vapors.  —  A  gas  is  matter  in  such  a  con- 
dition that  it  has  a  tendency  to  expand  indefinitely.     Gases 
have  no  independent  shape,  but  take  the  form  of  the  vessel 
in  which  they   are   confined.     Great   pressure   and   a  low 
temperature  are  required  to  change  most  gases  into  the 
liquid  state.     The  name  vapor  is  given  to  gaseous  matter 
that  is  liquid  or  solid  at  normal  temperatures  and  pressures. 
Water  vapor  is  an  example  of  vapor,  while  atmospheric  air 
is  a  familiar  form  of  gas,  and  will  be  used  in  studying  the 
phenomena  and  properties  of  gases. 

156.  Expansibility.  —  Demonstration.  —  Put  a  rubber  bag — 
a  toy  balloon  will  answer  —  under  the  receiver  of  an  air  pump, 
having  first  blown  a  little  air  into  it  and 

tied  the  stem.  Exhaust  the  air,  and  the 
balloon  will  be  seen  to  increase  in  size.  It 
will  do  this  as  long  as  air  is  pumped  from 
the  receiver. 

This  expansion  of  the  air  is  best  ex- 
plained by  the  kinetic  theory  of  gases 
(§  6) :  The  molecules  of  a  gas  are  in 
rapid  motion  in  straight  lines,  and  they 
continue  to  move  in  their  paths  until 
turned  aside  by  striking  either  other 
molecules  or  the  side  of  the  containing 
vessel.  When  the  balloon  is  put  under 

157 


FIG.  138 


158  GASES 

the  receiver  of  the  air  pump,  the  number  of  molecules  of 
air  per  cubic  centimeter  is  the  same  inside  it  as  outside 
of  it,  and  the  bombardment  of  the  molecules  on  one  side 
neutralizes  that  on  the  other,  so  the  walls  of  the  bag  remain 
as  they  are.  As  soon  as  air  is  taken  from  the  receiver,  how- 
ever,  the  number  of  molecular  blows  on  the  inside  exceeds 
the  number  on  the  outside  for  the  same  surface,  and  the  bag 
is  stretched  out  until  they  are  equal.  This  means  that  there 
are  again  the  same  number  of  molecules  in  the  same  space 
both  inside  and  outside,  or,  the  density  is  the  same.  If  now 
the  air  is  let  into  the  receiver,  the  blows  on  the  outside  in- 
crease and  the  bag  shrinks  to  its  original  size,  beaten  down 
by  the  impact  of  the  molecules  of  the  outside  air.  The  com- 
bined effect  of  the  impact  of  the  molecules  of  air  inside  the 
bag  makes  up  the  internal  pressure  of  the  air. 

157.  Compressibility.  —  In  order  to  show  the  great  com- 
pressibility of  gases,  it  is  only  necessary  to  apply  force  to 
an  air-tight  piston  moving  in  a  cylinder  closed  at  one  end. 
It  can  be  shown  in  a  very  simple  way  by  pushing  the  open 
end  of  a  long  test  tube  below  the  surface  of  water.     It  will 
be  found  that  the  deeper  the  tube  is  thrust  into  the  water, 
the  higher  the  water  rises  within  it;  and  the  more. the  air 
is  compressed,  the  greater  is  the  pressure  required  to  force  the 
tube  into  the  water. 

158.  Elasticity.  —  Gases  are  not  only  compressible,  but 
perfectly  elastic  under  compression. 

Demonstration.  —  Raise  the  piston  of  a  bicycle  pump  to  the  top, 
then  close  the  tube  leading  from  the  pump  and  force  the  piston  down. 
A  sharp  push  will  bring  it  nearly  to  the  bottom,  showing  a  compres- 
sion of,  say,  nine  tenths.  Now  let  the  piston  go,  and  it  will  rise  again 
to  the  top  of  the  pump. 


GASES 


159 


The  elasticity  of  gases  differs  from  that  of  solids  in  that 
it  is  elasticity  of  volume  and  not  of  form.  Gases  are  said 
to  be  perfectly  elastic  because  they  have  no  elastic  limit 
(§  17) ;  but  their  elasticity  is  not  very  great  as  measured  by 
Formula  1. 

159.  The  Air  Pump  is  an  instrument  used  for  removing- 
the 'air  from  any  vessel  with  which  it  is  connected.  The 
possibility  of  doing  this  depends  entirely  upon  the  fact  that 
air  is  elastic.  A  simple  air  pump  consists  of  a  cylinder  A 


FIG.  139.  —  Air  Pump 

(Fig.  139),  in  which  moves  a  piston  attached  to  the  rod  B~ 
A  tube  C  connects  this  cylinder  with  a  receiver  D,  from 
which  the  air  is  to  be  removed.  There  are  two  valves  be- 
tween the  air  in  D  and  the  external  air :  one  in  the  base  of 
the  cylinder,  and  the  other  in  the  piston.  These  open 
upward,  allowing  the  air  to  move  in  one  direction  only. 


160 


GASES 


At  E  there  is  a  stopcock  so  arranged  that  it  will  permit  free 
passage  for  the  air  between  the  pump  and  the  receiver,  or  cut  the 
receiver  off  altogether.  F  is  an  air-tight  glass  tube  which  com- 
municates with  the  receiver,  and  contains  a  closed  manometer  (see 
§  179,  6)  for  measuring  the  degree  of  exhaustion. 

The  operation  of  the  air  pump  is  as  follows :  Sup- 
pose the  piston  to  be  at  the  top  of  its  stroke.  The  first 
movement  downward  will  slightly  compress  the  air  under 
it.  This  closes  the  valve  at  the  base  of  cylinder  A  and  opens 
the  valve  in  the  piston.  The  air  passes  through  this  valve, 
and  when  the  piston  is  at  the  bottom  of  its  stroke,  the  air  in 
the  cylinder  is  above  it.  As  soon  as  the  piston  is  raised, 
the  pressure  below  it  is  decreased  and  the  valve  is  closed, 
and  as  the  piston  rises,  the  air  is  forced  out  of  a  hole  in  the 
top  of  the  cylinder,  or  through  the  small  tube  G.  The  cylin- 
der below  the  piston  is  filled  with  air  expanding  from  D. 
Each  stroke  is  only  a  repetition  of  the 
first,  except  that  the  amount  of  air 
taken  out  diminishes  with  every  stroke. 

160.  The  Fleuss  Pump.  —  One  of  the 
most  satisfactory  mechanical  air  pumps 
is  the  Fleuss  or  Geryk  pump,  a  diagram 
of  which  is  shown  in  Fig.  140,  while 
Fig.  141  shows  the  pump  itself.     The 
cylinder  is  separated  into  two  compart- 
ments by  a  diaphragm  D.     There  is  an 
opening   in   this  diaphragm,  which  is 
closed  by  a  collar  C,  through  which 
passes  the  piston  rod,  forming  an  air- 
tight joint.     The  collar  is  kept  down  by  the  pressure  of  a 
spring  S,  and  the  lower  part  of  each  compartment  is  filled 
with  a  heavy  oil.     When  the  piston  is  raised,  the  valve  V 


GASES 


161 


FIG.  141.  —  Fleuss  Pump 


closes,  the  oil  above  it  is  raised  and  the  air  compressed, 
until  the  shoulder  on.  the  piston  strikes  C  and  raises  it, 
when  the  air  and  a  part  of  the 
oil  pass  through  into  the  upper 
chamber.  When  the  piston  is 
lowered,  a  part  of  the  oil  runs 
back  to  the  lower  compartment, 
but  the  air,  being  above  the  oil, 
cannot  run  through.  The  cham- 
ber B  is  connected  to  the  space 
from  which  the  air  is  to  be  ex- 
hausted. The  tube  T  connects 
B  with  the  cylinder  below  the 
piston,  thus  preventing  the  for- 
mation of  a  vacuum  there  when 
the  piston  rises.  The  oil  makes  the  valves  air-tight,  so 
that  this  pump  is  easy  to  work  and  of  high  efficiency. 

161.  Uses  of  the  Air  Pump.  —  There  are  many  practical 
uses  of  the  air  pump,  among  them  its  application  to  "  vacuum 
pans "  for  the  making  of  sugar,  in  which 
the  pressure  is  kept  low,  so  that  evaporation 
will  take  place  at  a  lower  temperature  and  the 
sugar  will  not  be  burned.  Another  important 
use  of  the  air  pump  is  in  the  manufacture  of 
incandescent  lamps  and  thermos  bottles. 

162.  The  Condensing  Pump. — If  the  valves 
in  the  pump  shown  in  Fig.  139  were  arranged 
to  open  downward  instead  of  upward,  the 
pump  would  be  a  condenser.  When  it  is  nec- 
essary, however,  to  transfer  a  gas  from  one 
vessel  to  another,  an  arrangement  like  that 


FIG.  142 
Rev. 


162 


GASES 


shown  in  Fig.  142  is  used.  In  this  pump  the  piston  head 
has  no  valve.  The  pipe  P  is  attached  to  the  gas  supply, 
and  the  valve  in  P  opens  toward  the  cylinder. 
The  pipe  P'  is  attached  to  the  vessel  in  which 
the  gas  is  to  be  compressed,  and  its  valve  opens 
away  from  the  cylinder. 

The  valveless  bicycle  pump,  Fig.  143,  consists 
of  a  tube,  to  one  end  of  which  there  is  fixed  a 
piston  head  carrying  a  concave  leather  collar. 
When  the  cylinder  is  drawn  back,  the  air  passes 
around  the  collar,  but  when  it  is  pushed  forward 
the  collar  fills  the  cylinder,  the  air  is  compressed, 
and  passes  through  the  tube  into  the  tire. 

163.  Uses  of  Compressed  Air. — Pascal's  Law 
of  the  equal  transmission  of  liquid  pressure  may 

JIG.  14o 

be  applied  to  gases  as  well;  hence  compressed 
air  may  be  applied  to  the  transmission  of  power.  There 
are  many  machines  in  which  a  practical  application  of  such 
transmission  is 
used.  Riveting 
hammers  are  used 
for  forming  the 
rivet  heads  on  steel 
work.  Pneumatic 
tools  are  also  used 
in  stone  cutting, 
calking  the  seams 
of  ships  and  the 
joints  of  water 


piston ;   B,  hammer ;   C,  trigger  for 
turning  on  air ;   D,  air  pipe. 


FIG.  144.  —  Riveting  Hammer 


pipes,    iron   chipping,  drilling,  and  the  like.     Rock  drills, 
sand    blasts  for   cleaning   metal    surfaces,   railroad    signal 


GASES 


163 


operation,  and  submarine  work  are  other  common  appli- 
cations of  the  use  of  compressed  air. 


164.  The  Gas  Holder.  -  -  An  important  application  of  the 
transmission  of  pressure  by  gases  is  made  in  the  transmission 
of  the  gas  itself  in  the  delivery  of  illuminating  gas  from  the 
gaspmeter,  or  gas  holder,  to  the  delivery  pipes.  Figure  146 
shows  how  this  is  done  and  gives  a  cross  section  of  the  gas 
holder,  which  consists  of  an  inverted  bowl  of  steel,  the  edge 
of  which  dips  below  the  surface  of  water.  Pumps  force 
the  gas  into  the  holder  from  the  retorts  where  it  is  made. 
Since  the  holder  is  supported  by  the  gas  underneath  it,  the 
weight  of  the  holder  produces  the  pressure  that  forces  the 
gas  through  the  service  pipes. 

The  sections  of  the  holder  work  within  one  another  some- 
what like  the  sections  of  a  telescope. 
A  circular  trough  is  bolted  on  the  out- 
side of  the  upper  section  at  its  lower 
edge  (Fig.  146)  and  is  filled  with  water. 
An  inverted  trough  is  fastened  to  the 
inside  of  the  next  section  below  at  its 
upper  edge  in  such  a  way  that  when 
the  upper  section  is  filled  with  gas 
and  rises,  the  two  sections  are  coupled 
together  by  the  lips  of  the  troughs, 
which  form  a  water  seal  (Fig.  145). 

When  the  weight  of  the  second  sec- 
tion is  added  to  that  of  the  first,  the 
pressure  on  the  gas  is  increased ;  a  Ln0sJ,deer  section 

governor     is    therefore  placed   in   the 
delivery  pipe  to  equalize  the  pressure. 

mi  FIG.  145.  — Cross  Sec- 

Ihe  weight  of  the  upper  section  must       tion  of  Water  Seal 


Trough 


164 


GASES 


PRESSURE       REGULATING 
GOVERNOR 

IN  SMALL   GOVERNOR    MOUSE. 


FIG.   146.  —  Diagram  of  a  Gas  Supply  System 


GASES 


165 


be  great  enough  to  give  the  required  pressure  to  the  gas 
when  the  other  sections  are  not  in  use. 

165.  Weight. — Though  gases  are  the  lightest  forms  of 
matter,  each  has  weight,  as  may  be  found  by  weighing. 

Demonstrations.  —  Weigh  on  a  delicate  balance  a  light  glass  flask 
that  is  fitted  with  a  stopcock.  Exhaust  the  air  from  the  flask 
and  weigh  it  again,  and  the  flask 
and  contents  will  be  found  to  be 
lighter  than  before. 

Weigh  carefully  an  incandes- 
cent lamp  bulb.  One*  with  a 
broken  filament  will  answer,  and 
one  with  a  light  base  is  desirable. 
Direct  the  point  of  a  blowpipe 
flame  upon  one  side  of  the  bulb. 
As  soon  as  the  glass  becomes  red- 
hot  it  is  forced  in  by  the  pressure 
of  the  atmosphere,  and  if  only  the 
point  of  the  flame  is  used,  a  small, 
round  hole  will  be  blown  in  the 
bulb.  The  filament  will  probably  be  blown  in  pieces,  but  the  pieces 
will  all  be  inside  the  bulb,  and  there  will  be  no  loss  of  weight  on 
account  of  losing  any  of  them.  Weigh  the  bulb  a  second  time, 
and  the  difference  in  weight  will  be  the  weight  of  the  air  that  has 
entered  the  bulb. 

By  an  extension  of  these  methods  the  weight  of  air  and 
other  gases  has  been  found.  The  weight  of  1  c.c.  of  dry 
air  at  0°  C.  and  the  barometric  pressure  of  760  mm.  is 
0.001293  g.  Since  1  c.c.  of  water  at  0°  C.  weighs  practically 
1  g.,  the  weight  of  air  is  y^  of  the  weight  of  water. 

Hydrogen,  the  lightest  known  gas,  weighs  0.0000899  g.  per  cubic 
centimeter;  hence  air  is  about  14.4  times  as  heavy  as  hydrogen. 
The  weight  of  air  in  English  measure  is  0.33  grain  per  cubic  inch, 
of  hydrogen  0.0228  grain,  and  of  carbon  dioxide  0.5046  grain. 


FIG.  147 


166  GASES 

166.  Composition  of  the  Atmosphere.  —  The  air  composing 
the  atmosphere  of  the  earth  is  a  mixture  of  gases.      About 
J  by  volume  is  oxygen,  f  nitrogen,  ^Vfr  carbon  dioxide,  and 
a  variable  proportion  aqueous  vapor. 

The  quantity  of  aqueous  vapor  depends  greatly  upon  the  tem- 
perature ;  it  varies  from  4.835  g.  or  less  per  cubic  meter  at  0°  C.,  to 
22.796  g.  or  less  per  cubic  meter  at  25°  C. 

Besides  the  above,  there  are  traces  of  other  common  gases,  as 
ammonia  and  ozone,  and  small  quantities  of  several  recently  dis- 
covered gases.  Argon  was  discovered  in  1895  by  Lord  Rayleigh 
and  Professor  Ramsay  as  the  result  of  an  admirable  course  of 
scientific  research.  It  forms  nearly  ^  of  the  atmosphere.  After 
its  discovery,  Professor  Ramsay  continued  his  researches,  and 
discovered  four  other  gases  in  the  atmosphere,  —  helium,  neon, 
krypton,  and  xenon.  These  are  present  in  minute  quantities  only, 
and  are  isolated  by  the  employment  of  low  temperatures. 

167.  Pressure  of  the  Atmosphere.  —  Since  air  has  weight, 
the  layers  of  air  near  the  surface  of  the  earth  are  subject 
to  a  pressure  due  to  the  weight  of  the  air  above. 

Demonstrations.  —  Tie  a  sheet  of  thin  rubber  over  one  end  of  a 
bladder  glass  (Fig.  148)  and  place  it  on  the  plate  of  an  air  pump. 

Remove  a  part  of  the  air  below  the 
rubber  by  a  stroke  or  two  of  the  pump. 
The  rubber  will  be  pushed  inside  the 
glass.  What  supports  the  downward 
pressure  of  the  air  before  the  pump  is 
worked  ? 

Cut  off  the  stem  of  a  thistle  tube 
about  4  in.  from  the  cup.  Tie  a  thin 
rubber  sheet  over  the  cup.  Slip  over 
the  stem  a  flexible  rubber  tube,  and 
draw  out  some  of  the  air  by  suction. 
plQ  14g  Pinch  the  rubber  tube  to  keep  the 

pressure  constant.  Hold  the  cap  in 
different  positions  (Fig.  149),  and  it  will  be  seen  that  the  air 
presses  equally  in  all  directions. 


GASES 


167 


Fill  a  tumbler  full  of  water.     Slide  a  heavy  card  over  the  top  of 

the  tumbler,  being  careful  that  no  air  bubbles  are  left  below  it. 

Hold  the  card  while  you 

invert  the  tumbler.  Re- 
move the  support  from 

the  card,  and  it  will  re- 
main   pressed     against 

the,  tumbler,  holding  in 

the   water.      Hold   the 

card   on  and  turn  the 

tumbler  so  that  the  card 

is    vertical;    when   the 

hand    is    removed,    the  FIG.  149 

card  still  remains. 

Select  a  long,  clear  glass  bottle  and  fit  to  the  neck  a  rubber  stopper 

with  one  hole.  Pass  through  this  a  short  glass  tube  with  the  inner 
end  drawn  down  to  a  fine  opening.  Fit  one 
end  of  a  rubber  tube  to  the  outer  end  of  the 
glass  tube  and  connect  the  other  end  to  the  air 
pump.  Exhaust  the  air.  Pinch  the  tube  to- 
gether; hold  the  bottle  as  in  Fig.  150,  and 
pull  the  rubber  from  the  glass  tube  when  it 
is  below  the  surface  of  the  water  in  the  dish 
A.  The  pressure  of  the  air  upon  the  surface 
of  the  water  will  force  a  stream  through  the 
tube,  forming  a  fountain  inside  the  bottle, 
and  the  water  will  continue  to  flow  until  the 
cmount  of  water  in  the  bottle  is  equal  to  the 
volume  of  air  taken  out.  This  is  a  very 
old  experiment,  called  the 
fountain  in  vacuo. 
Procure  two  small  bottles  and  put  into  each 

the  end  of  a  U-tube,  fitting  loosely  in  B  (Fig.  151), 

and    air-tight   through  a  rubber  stopper   in  A. 

Fill  A  half  full  of  water;   place  both  under  the 

receiver  of  an  air  pump  and  exhaust  the  air. 

At  the  first  stroke  the  water  from  A  will  begin  to 

run  into  B.    Explain.  FIG.  151 


FIG.  150 


168  GASES 

Exhaust  until  nearly  all  the  water  is  drawn  over,  and  then  let 
air  into  the  receiver.  The  water  will  run  back  into  A.  Explain. 

168.  The  Buoyant  Force  of  the  Atmosphere.  —  A  body 
submerged  in  water  is  buoyed  upward  by  a  vertical  upward 
force  that  is  equal  to  the  weight  of  the  displaced  water. 
This  pressure  amounts  to  62.5  Ib.  for  each  cubic  foot  of  the 
volume  of  the  submerged  body.     Since  the  air  has  weight, 
a  body  is  buoyed  up  by  it  in  the  same  way.     The  amount 
of  the  lifting  force  is  as  much  less  than  that  produced  by 
water  as  the  air  is  lighter  than  water.     Air  at  sea  level  weighs 
TY3  of  the  weight  of  water,  or  about  0.08  Ib.  per  cubic  foot. 
This  means  that  the  lifting  power  of  the  air  on  a  spherical 
balloon  20  ft.  in  diameter  is  over  338  Ib.  at  the  surface  of 
the  earth.     As  the  rarity  of  the  air  increases  with  the  distance 
from  the  earth,  the  lifting  power  is  less  at  high  altitudes. 

169.  The    Airplane.  —  The    aeroplane    or    airplane    is    a 
heavier-than-air  machine  which  is  lifted  by  the  thrust  of 
the  air  upon  the  under  sides  of  its  planes  when  they  are  driven 
through  it  at  high  speed.     This  speed  is  secured  by  the  push 
of  a  light  screw  propeller  that  rotates  very  rapidly,  being 
driven  by  a  special  form  of  gasoline  engine. 

The  four  main  parts  of  an  airplane  are:  (1)  the  principal 
planes,  wings,  or  glider  unit ;  (2)  the  body  unit ;  (3)  the  t?,il 
unit;  (4)  the  undercarriage  or  chassis. 

Airplanes  are  monoplanes,  biplanes,  or  triplanes,  dependent 
upon  the  number  of  principal  planes.  The  ailerons,  or  wing 
flaps,  are  usually  placed  at  each  wing  tip  and  are  used  to 
stabilize  the  airplane  and  to  bank  or  tip  it  out  of  the  hori- 
zontal position  in  turning. 

The  body  of  the  airplane  contains  the  engine,  fuel,  pilot, 
passengers,  and  load.  If  the  airplane  is  of  the  tractor  type, 


GASES 


169 


FIG.  152. — 


The  American  Seaplane  NC  4  in  Flight ;  the  first  Airplane 
that  flew  across  the  Atlantic  Ocean  (1919) 


FIG.  153.  —  A  Close-up  View  of  the  NC  4,  Showing  the  Wings  and  Body 


170 


GASES 


having  its  propeller  in  front,  the  body  is  extended  backward 
to  support  the  tail  planes  and  is  called  the  fuselage. 

The  tail  unit  consists  of  both  horizontal  and  vertical 
planes.  These  are  movable  and  are  under  the  control  of 
the  pilot.  They  serve  both  to  stabilize  the  airplane  and  to 
control  the  direction  of  its  flight.  A  change  in  the  position 
of  the  horizontal  tail  plane  changes  the  altitude  of  the  air- 
plane by  pointing  its  nose  upward  or  downward,  while  a 
change  in  the  position  of  the  vertical  tail  plane  changes  its 
line  of  flight  either  to  the  right  or  to  the  left. 

The  undercarriage,  or  chassis,  usually  consists  of  one  or 
more  pairs  of  wheels  in  front  and  a  skid  in  the  rear.  These 
are  used  for  running  over  the  surface  of  the  ground  at  the 
beginning  of  a  flight  until  enough  speed  is  attained  to  enable 
the  plane  to  rise  into  the  air ;  they  are  also  used  in  landing 
at  the  end  of  a  flight. 


FIG.  154.  —  Airplane  Instruments 

A,  ignition  switch;  B,  light  switches;  C,  pressure  pumps;  D,  revolution  counter 
showing  the  number  of  revolutions  of  the  propeller;  E,  map;  FG,  control  wheel;  H, 
altimeter  indicating  height;  /,  oil  pressure  gauge;  J,  barometer;  K,  compass;  L,  air 
speed  indicator ;  M,  gas  throttle. 


GASES 


171 


FIG.  155 


In  seaplanes  (Fig.  152)  the  wheels  and  skids  are  replaced 
by  floats  that  help  to  support  the  body  of  the  plane  above 
the  surface  of  the  water.  Figure  154  shows  a  number  of  the 
most  useful  instruments  used  by  the  pilot  of  an  airplane. 

170.  Measurement    of    Atmospheric    Pressure.  — While 

the  above  experiments  have  demonstrated  the  existence  of 

atmospheric  pressure,  they  have  given 

no  accurate  idea  of  its  amount.     The 

principle  employed  in  finding  its  amount 

is  the  same  as  that  of  balancing  columns 

used  in  finding  the  specific  gravity  of 

liquids.     If  a  bottle  is  filled  with  water 

and  inverted  with  its  mouth  under  the 

surface,  as  in  Fig.  155,  the  water  will 

remain  in  the  bottle.     The  downward 

pressure  of  water  in  the  bottle  A  is 

counterbalanced  by  the  downward  pressure  of  the  air  upon 
the  surface  of  the  water  in  B,  since  the  down- 
ward pressure  upon  the  surface  is  transmitted 
into  an  upward  pressure  at  the  mouth  of  the 
bottle. 

In  order  to  balance  the  entire  pressure  of  the 
atmosphere  by  a  water  column,  the  bottle  in 
Fig.  155  would  need  to  be  extended  into  a  tube 
about  34  ft.  long ;  but  by  using  a  liquid  heavier 
than  water,  a  correspondingly  shorter  tube  can 
be  used. 

Demonstration.  —  Close  one  end  of  a  glass  tube 
80  cm.  long  and  about  6  mm.  in  internal  diameter. 
Fill   it  nearly  full  with  clean  mercury.     Close  the 
open  end  with  the  finger,  and  invert  it  several  times 
FIG.  156      to  remove  all  air  bubbles  clinging  to  the  sides  of  the 


172  GASES 

tube.  Now  fill  the  tube  full,  put  a  finger  over  the  open  end,  in- 
vert it,  and  place  the  open  end  beneath  the  surface  of  mercury  in 
a  dish.  Remove  the  finger  carefully  so  that  no  air  shall  get  into 
the  tube.  The  mercury  will  fall  a  little,  and  the  height  at  which 
it  stands  will  measure  the  atmospheric  pressure  (Fig.  156). 

171.  Atmospheric  Pressure  at  Sea  Level.  —  The  average 
height  at  which  the  mercury  column  stands,  at  the  level  of 
the  sea,  is  76  cm.,  and  this  height  is  independent  of  the  di- 
ameter of  the  tube.     If  the  area  of  the  cross  section  of  the  tube 
is  1  sq.  cm.,  the  volume  of  the  mercury  will  be  76  c.c.,  and 
since  its  specific  gravity  is  13.596,  its  weight  will  be  1033.3  g. 
In  English  measure  the  average  height  of  the  column  is  30  in., 
and  if  its  cross  section  is  1  sq.  in.,  its  weight  will  be  14.7  Ib. 
Since  this  weight  is  the  measure  of  the  pressure  of  the  air,  we 
can  state  the  following :    • 

The  average  pressure  of  the  atmosphere  at  sea  level  is  14.7  Ib. 
per  square  inch,  or  1033.3  g.  per  square  centimeter.  This  is 
called  a  pressure  of  1  atmosphere,  and  as  it  is  constantly 
changing,  it  is  often  called  in  round  numbers  15  Ib.  per  square 
inch,  or  1  kg.  per  square  centimeter. 

172.  The  Barometer.  —  The  experiment  with  the  glass 
tube  filled  with  mercury  was  first  made  by  Torricelli  in  1643, 
and  the  space  above  the  mercury  column  in  the  tube  is  called 
a  Torricellian  vacuum. 

The  mercurial  barometer  consists  of  a  glass  tube  about  34 
in.  long,  filled  with  mercury,  and  inverted  with  its  lower  end 
constantly  below  the  surface  of  mercury  in  a  cistern.  It  is 
fixed  in  a  vertical  position  with  a  scale  C  graduated  along  the 
top  near  the  end  of  the  mercury  column,  the  zero  of  this 
scale  being  the  surface  B  of  the  mercury  in  the  cistern  A  at 
the  bottom  (Fig.  157). 


GASES 

In  reading  the  barometer  a  vernier  scale  is 
generally  used  to  secure  accuracy.  The  ver- 
nier must  be  brought  to  the  top  of  the  con- 
vex surface  of  the  mercury,  and  the  eye  must 
be  on  a  horizontal  line  from  the  top  of  the 
column;  this  may  be  secured  by  placing  a 
smalL  vertical  mirror  behind  the  top  of  the 
column,  and  placing  the  eye  so  that  its  image 
and  the  top  of  the  column  coincide.  Before 
the  height  is  read,  the  surface  of  the  mercury 
in  the  cistern  must  be  brought  to  the  fixed 
zero.  This  is  done  by  turning  the  screw  c 
which  raises  or  lowers  the  mercury  in  the 
cistern  until  it  just  touches  the  point  of  a 
pin  projecting  downward  from  the  frame  of 
the  instrument,  which  point  is  the  zero  of 
the  scale. 

If  a  liquid  less  dense  than  mercury  is 
used,  the  column  will  be  correspondingly 
longer,  and  changes  in  it,  caused  by  changes 
in  atmospheric  pressure,  will  be  correspond- 
ingly greater.  The  glycerin  barometer  has  a 
height  of  about  27  ft.,  and  a  change  of  nearly 
11  in.  for  every  change  of  1  in.  in  the  mercury 
barometer. 

173.  The  Aneroid  Barometer  takes  its  name 
from  two  Greek  words  meaning  "  without 
fluid."  It  consists  of  a  circular  box  of  thin 
metal,  with  corrugated  sides,  a  cross  section 
of  which  is  shown  in  Fig.  158.  One  side  of 
the  box,  or  vacuum  chamber,  as  it  is  called, 


173 


m 


174 


GASES 


FIG.  158 


is  firmly  fixed  to  the  base  of  the  instrument.     The  air  is 
partly  removed  from  the  box  and  it  is  sealed  air-tight. 

Variations  in  the  atmos- 
pheric pressure  cause 
corresponding  changes  in 
the  position  of  the  elastic 
upper  face  of  the  vacuum 
chamber,  and  these 
changes  are  transmitted 
by  a  system  of  delicate  levers  to  a  pointer  which  moves 
around  a  graduated  dial.  The  readings  of  this  dial  are 
made  to  correspond  to  those  of  a 
standard  mercury  barometer. 

These  instruments  are  very  delicate 
and  will  show  a  variation  in  reading  on 
being  raised  from  the  floor  to  a  table; 
for  the  atmospheric  pressure  varies  not 
only  with  the  weather  bid  also  with  the 
elevation  above  sea  level.  If  an  aneroid 
barometer  is  carried  in  an  elevator  from 
the  street  floor  to  the  top  floor  of  a 
high  building,  the  decrease  of  air  pres- 
sure from  floor  to  floor  is  readily  seen. 
It  is  on  account  of  this  decrease  in  at- 
mospheric pressure  that  the  pressure  of  illuminating  gas  is  appar- 
ently greater  at  the  top  of  a  building  than  at  the  base.  The  pres- 
sure forcing  the  gas  from  the  tube  is  the  difference  between  the 
pressure  in  the  pipes  and  the  pressure  of  the  air.  Since  the  air 
pressure  is  greatest  at  the  base  of  the  building,  the  excess  pressure 
of  the  gas  is  greater  at  the  top. 

The  barograph  (Fig.  160)  is  an  aneroid  barometer  with  attach- 
ments that  make  a  permanent  record  of  its  readings. 

174.   Weather  Indicated  by  the  Barometer.  —  A  constant 
use  of  the  barometer  is  made  in  the  Weather  Bureau  in  fore- 


FIQ.  169. — Aneroid  Barom- 
eter 


GASES 


175 


FIG.  160.  —  Barograph 

casting  changes  in  the  weather.     The  relation  of  barometric 
readings  to  the  state  of  the  weather  may  be  stated  as  follows  i 

I.  A  rising  barometer  precedes  fair  weather. 

II.  A  falling  barometer  precedes  foul  weather. 

III.  A  sudden  fall  in  the  barometer  precedes  a  storm. 

IV.  An  unchanging  high 
barometer     indicates     settled 
fair  weather. 

175.  Cyclonic  Storm  Pres- 
sure. —  The  relation  be- 
tween the  readings  of  the 
barometer  and  the  direction 
of  the  wind  in  circular  or 
cyclonic  storms  may  be 
studied  in  connection  with 
the  weather  map,  Fig.  161. 
At  the  center,  or  eye  of 
the  storm  (marked  LOW),  FlG- 161 

the  pressure  is  least ;    while  at  the  outside  the  pressure  is 
greater,  and  the  air  therefore  rushes  toward  the  center.     In 


176  GASES 

the  northern  hemisphere  winds  are  deflected  to  the  right 
by  the  rotation  of  the  earth.  In  approaching  the  center 
of  low  pressure,  therefore,  the  direction  of  each  air  current 
is  to  the  right  of  the  center.  This  gives  to  the  storm  a 
rotary  motion  in  a  counter-clockwise  direction;  and  if 
a  person  stands  with  his  back  to  the  wind,  the  storm  cen- 
ter, or  region  of  lowest  barometer,  will  be  on  his  left 
hand. 

The  observations  of  the  Weather  Bureau  on  barometric  pres- 
sures for  a  series  of  years  indicate  that  there  is  a  well-defined  move- 
ment of  low  pressures,  or  storm  centers,  across  the  continent.  These 
areas  of  low  pressure  generally  enter  the  United  States  on  the 
northwest  boundary,  coming  from  British  America,  move  south- 
eastwardly  until  they  have  crossed  the  Rocky  Mountains,  and  then 
turn  northeastwardly  and  disappear  on  the  Atlantic  coast,  or  pass 
down  the  St.  Lawrence  River.  The  storms  that  come  into  the  coun- 
try from  the  Gulf  of  Mexico  usually  travel  northeast  along  the 
Altantic  coast. 

176.  Height  of  the  Atmosphere.  —  The  compressibility  of 
the  air  is  so  great  that  the  layer  in  contact  with  the  surface 
of  the  earth  is  more  dense  than  the  layers  above  it.  Though 
the  density  constantly  decreases  as  the  distance  from  the 
earth  increases,  no  uniform  rule  can  be  given  that  will  show 
the  relation  between  barometric  readings  and  the  corre- 
sponding heights  of  the  atmosphere.  However,  a  fall  of  one 
inch  in  the  mercury  column,  from  the  reading  at  sea  level, 
indicates  an  elevation  of  about  900  ft. 

Figure  162  is  a  graph  showing  the  relation  (in  fair  weather) 
between  height  above  the  surface  of  the  earth  in  feet  and 
the  pressure  of  the  atmosphere  as  measured  by  inches  of 
mercury.  It  is  seen  from  this  curve  that  at  a  height  of 
20,000  ft.  the  pressure  is  reduced  from  31  in.  of  mercury  to 


OASES 


177 


less  than  15,  which  means  that  the  density  of  the  air  is  not 
half  so  great  at  that  height  as  at  the  surface. 


20 


LU 

I  10 


HEIGHT   IN    FEET 
FIG.  162. — Atmospheric  Pressure  at  Different  Heights 

Balloon  ascensions  have  exceeded  this  height,  notably  that  of  Mr. 
James  Glaisher,  undertaken  for  the  purpose  of  making  scientific 
observations  for  the  British  Association  for  the  Advancement  of 
Science.  Both  Mr.  Glaisher  and  his  aeronaut,  Mr.  Coxwell,  became 
unconscious,  but  before  losing  consciousness  succeeded  in  letting 
enough  gas  escape  to  bring  the  balloon  down  into  the  denser  atmos- 
phere. The  pressure  recorded  by  the  instruments  indicated  a 
height  of  37,000  ft.  The  height  of  36,020  ft.  was  reached  on  Feb- 
ruary 27,  1920,  by  Major  R.  W.  Schroeder,  who  drove  an  airplane 
from  McCook  field,  Dayton,  Ohio.  The  extreme  cold  at  this  height 
rendered  him  temporarily  blind.  His  machine  fell  five  miles  but 
was  righted  at  2000  feet  and  made  a  safe  landing. 

177.  Boyle's  Law.  —  Since  an  increase  of  pressure  reduces 
the  volume  of  a  gas,  it  is  important  to  know  whether  there  is 
a  definite  relation  between  the  pressure  exerted  upon  a  gas 
and  the  resulting  volume.  This  was  experimentally  deter- 

Rev. 


178 


GASES 


mined  independently  by  two  physicists,  Boyle  and  Mariotte. 
The  results  obtained  were  formulated  in  what  is  called 
Boyle's  Law,  which  may  be  stated  as  follows : 

The  temperature  remaining  the  same,  the  volume  of  a  given 
mass  of  gas  varies  inversely  as  the  pressure  acting  upon  it. 
This  may  be  expressed  by  the  proportion  V :  V  =  P' :  P, 
from  which  we  get  DT7  _  D/T7,  (4Q) 


PV  =  P'V, 

i.e.,  PV  =  a  constant  quantity. 

The  mass  of  the  air  remaining  the  same,  it  is  evident  that 
the  density  must  increase  as  the  volume  diminishes ;  hence, 

At  a  constant  temperature  the  density  of  a  gas  is  directly 
proportional  to  the  pressure  acting  upon  it. 

Very  careful  measurements  show  that  gases  do  not  obey  Boyle's 
Law  exactly,  and  that  different   gases  behave  differently  in  this, 
respect.     But  for  practical  purposes  the  law  may 
be  considered  to  hold  true,  except  at  tempera- 
tures so  low  that  the  gas  is  about  to  liquefy. 


86- -: 


178.  Verification  of  Boyle's  Law.— (a)  For 
Pressures  Greater  than  One  Atmosphere.  — 
Demonstration.  —  Bend  a  glass  tube  as  shown 
in  Fig.  163,  the  long  arm  being  open  and  the 
short  one  closed.  Fix  this  to  a  vertical  support 
and  place  a  graduated  scale  between  the  two 
arms.  Pour  mercury  into  the  long  arm  by 
means  of  a  long  funnel,  and  tip  the  tube  in  such 
a  way  as  to  let  bubbles  of  air  pass  from  the  short 
tube  into  the  long  one,  and  thus  bring  the  mer- 
cury to  the  same  level  AB  in  both.  This  line  is 
chosen  at  a  convenient  position,  say  20  cm. 
below  the  closed  end.  On  pouring  mercury  into 
the  long  tube  it  will  be  found  necessary  to  fill  it 
to  a  height  of  about  760  mm.  above  the  mercury  in  the  short 
tube  to  reduce  the  volume  of  the  gas  one  half.  The  pressure  upon 


.B 


FIG.  163 


GASES 


179 


FIG.  164 


the  mercury  in  the  short  tube  is  the  elastic  force  of  the  air  above  it, 
and  this  is  equal  to  the  pressure  above  the  line  CD  in  the  long  tube, 
which  is  two  atmospheres,  one  being  the  760  mm.  of 
mercury  and  the  other  the  free  atmosphere  above  it. 
State  how  this  proves  the  law. 

(6)  For  Pressures  Less  than  One  Atmosphere.  — 
Demonstration.  —  Fix  vertically  a  glass  tube  closed 
at  the  lower  end,  about  70  cm.  long  and  at  least 
8  mm.  in  internal  diameter.  Cut  off  a  piece  of  glass 
tubing  6  or  7  mm.  in  external  diameter  and  make 
three  marks  upon  it,  one  at  10  cm.,  one  at  20  cm., 
and  one  at  58  cm.  from  one  end.  Pour  mercury  into 
the  large  tube  until,  on  thrusting  the  smaller  tube 
into  it  with  the  10  cm.  mark  uppermost,  the  mercury 
will  rise  to  the  10  cm.  mark.  Place  the  ringer  over 
the  top  and  inclose  a  column  of  air  10  cm.  long. 
This  has  an  elastic  pressure  of  1  atmosphere  and  just 
balances  the  pressure  on  the  surface  of  the  mercury 
in  the  larger  tube.  Now  raise  the  smaller  tube  until 
the  mercury  sinks  to  the  20  cm.  mark  on  the  inside  of  the  tube ; 
what  is  now  the  elastic  pressure  of  the  in- 
closed air?  On  the  outside  the  mercury 
will  stand  nearly  at  the  58  cm.  mark.  Why  ? 

179.  The  Manometer  is  an  instru- 
ment for  measuring  the  pressure  of 
gases.  It  is  made  in  two  forms,  the 
open  and  the  closed. 

(a)  The  Open  Manometer  consists  of 
a  bent  glass  tube  held  in  a  vertical 
position  by  a  frame  having  a  gradu- 
ated scale  between  the  two  arms  of  the 
tube  (Fig.  165).  Mercury  or  some 
other  suitable  liquid  is  poured  into  the 
FIG.  165  manometer  so  that  it  stands  at  the 


180 


GASES 


A—  -7m      - 


0—  -U-- 


JE; — »_.  LJL. 


FIG.  166 


same  height  in  both  arms.  The  short  arm  is  connected 
with  the  vessel  containing  the  gas,  and  when  the  gas  is 
turned  on,  the  pressure  is  shown  by  the  difference  in  level 
of  the  columns.  The  length  of  the 
column  Of  liquid  CD  is  the  measure  of 
the  pressure  in  excess  of  1  atmosphere. 

(6)  The  Closed  Manometer  (Fig.  166), 
or  pressure  gauge,  differs  from  the  open 
manometer  in  being  closed  at  one  end 
and  much  shorter.  Before  the  pres- 
sure is  turned  on,  the  mercury  stands 
at  the  level  BDy  with  the  ordinary 
atmospheric  pressure  in  each  arm. 
When  the  stopcock  is  turned,  the  pres- 
sure of  the  gas  not  only  maintains  the  pressure  of  the 
mercury  column  CE,  but  also  compresses  the  volume  of 
air  from  AB  to  AC.  Pressure  gauges  are  calibrated  to 
show  the  pressure  in  excess  of  1  atmosphere. 

In  a  closed  manometer  sometimes  used  to  measure  small  pressures, 
the  closed  end  of  the  tube  is  entirely  filled  with  mercury  at  atmos- 
pheric pressure.  As  the  air  is  exhausted  from  the  vessel  with  which 
the  manometer  is  connected,  the  mercury  sinks  in  the  closed  end ; 
the  height  of  the  column  shows  the  pressure  just  as  a  barometer  does. 

180.  The  Siphon  is  a  bent  tube  with  arms  of  unequal 
length,  used  to  transfer  a  liquid  from  one  vessel  to  another 
at  a  lower  level  by  carrying  the  liquid  over  the  edge  of  the 
vessel.  A  flexible  rubber  tube  makes  a  very  convenient 
siphon. 

Demonstration.  —  Fill  a  siphon  tube  like  that  shown  in  Fig.  167 
with  water  and  close  the  end  of  the  long  arm  with  the  finger.  Invert 
it  and  place  the  end  of  the  short  arm  below  the  surface  of  water  in  a 


GASES 


181 


beaker.     The  water  will  begin  to  flow  at  once,  and  will  continue  to 
flow  until  the  water  in  the  beaker  is  below  the  end  of  the  tube. 

181.  Cause  of  the  Action  of  the  Siphon.  —  At  the  level  of 
the  water  surface  A  (Fig.  167),  the  upward  pressure  in  the 
short  arm  of  the  siphon  is  the  at- 
mospheric pressure,  while  the  down- 
ward pressure  is  the  weight  of  the 
water  column  AB.  The  upward 
pressure  at  the  point  D  is  also  the 
atmospheric  pressure,  and  the  down- 
ward pressure  is  the  weight  of  the 
water  column  DC.  The  resulting 
upward  pressure  at  any  point  will 
be  the  atmospheric  pressure  minus 
the  pressure  of  the  water  column  at 
that  point,  and  as  the  column  CD  is 
longer  than  the  column  AB,  the  re- 
sulting upward  pressure  at  A  is 
greater  than  at  D,  and  the  water  is 
forced  from  A  toward  D. 

It  is  evident  that  unless  the  pressure  due  to  the  liquid 
column  AB  is  less  than  the  pressure  of  the  atmosphere, 
there  will  be  no  flow  of  the  liquid.  Hence  a  siphon  cannot 
raise  water  more  than  34  ft.,  nor  mercury  more  than  30  in., 
when  the  barometer  stands  at  the  normal  height. 

The  final  resultant  of  the  pressures  depends  upon  the 
difference  in  the  heights  of  the  liquid  columns ;  hence  the 
greater  the  difference  in  height,  the  faster  will  be  the  flow. 

It  is  evident  that  the  size  of  the  tube  used  as  a  siphon 
does  not  affect  the  height  to  which  a  liquid  can  be  raised, 
since  both  the  downward  pressure  of  the  liquid  column  due 
to  its  weight  and  the  total  upward  pressure  of  the  atmos- 


FIG.  167.  — Siphon 


182 


CASKS 


phere  at  the  end  of  the  tube  are  directly  proportional  to  its 
area  of  cross  section. 

182.  The  Lifting  Pump.  —  There  is  practically  no  differ- 
ence between  the  suction  or  lifting  pump  and  the  simple 
air  pump.  In  both  the  valves  open  upward  and  should  be 
air-tight.  From  the  base  of  the  cylinder  of  a  lifting  pump 
a  tube  runs  to  the  water  supply,  and  near  the  top  of  the  cyl- 
inder is  a  spout  for  carrying  off  the  water.  When  the  pump 

is  started,  the 
air  is  first 
pumped  out. 
On  the  up 
stroke  of  the 
piston,  pressure 
is  removed 
from  the  top  of 
the  lower  valve 
and  atmos- 
pheric pressure 
causes  water  to 
rise  in  the  tube 
T,  finally  filling 
the  space  be- 
low the  piston. 
On  the  down  stroke  of  the  piston  the  lower  valve  closes, 
holding  the  water  above  it.  Water  is  forced  through  the 
piston  valve.  On  the  next  up  stroke  of  the  piston,  water  is 
lifted  out  (Fig.  169).  It  will  be  seen  that  the  upper  valve 
must  be  placed  so  that  its  highest  position  shall  not  be 
more  than  34  ft.  above  the  level  of  the  water  in  the  cistern. 
About  27  ft.  is  the  practical  limit. 


FIG.  168.  —  Down  Stroke 
of  Piston 


FIG.  169.— UpStroke 
of  Piston 


GASES 


183 


183.  The  Force  Pump,  like  the  condenser,  applies  pres- 
sure to  the  stream  sent  from  the  pump.     The  force  pump 
shown  in  Fig.  170  differs  from  the 

ordinary  lifting  pump  in  having 
the  upper  end  of  the  cylinder 
closed  water-tight,  and  in  the 
addition  of  the  valve  V  and  air 
chamber  A.  The  elasticity  of 
the  air  cushion  in  A  forces  the 
water  out  at  P  in  a  steady 
stream,  though  it  comes  in 
through  V  only  during  the  up- 
ward stroke  of  the  piston. 

184.  Centrifugal   and    Rotary 
Pumps.  —  In     centrifugal     and 
rotary  pumps,  the  moving  parts 
have  a  circular  motion  only,  in- 

stead  of  the  reciprocating  motion  ' Force  PumP 

of  the  piston  in  the  lifting  and  force  pumps.     A  centrifugal 
pump  is  a  reversed  turbine.     Any  reaction  turbine,  if  run 

backward  by  power 
applied  to  its  axle, 
will  force  water  up 
the  penstock.  The 
supply  pipe  for  a  cen- 
trifugal pump  delivers 
the  water  at  the 
171  middle  of  the  wheel, 

and      the     discharge 
pipe  opens  from  the  circumference  of  the  case. 

In  the  rotary  pump  there  are  two  wheels  with  interlocking 


184 


GASES 


spurs  that  rotate  in  opposite  directions.  Centrifugal  pumps 
are  used  to  furnish  a  circulation  of  cold  water  for  steam 
condensers.  Figure  172  shows  a  motor-driven  circulating 


FIG.  172.  —  A  48-Inch  Circulation  Pump,  60,000  G.  P.  M.,  20-Foot  Head 

pump  with  a  capacity  of  60,000  gallons  per  minute  through 
its  48-inch  discharge  pipe.  Various  forms  of  centrifugal 
pumps  are  used  in  vacuum  cleaners. 

185.   Absorption  of  Gases  by  Solids.  —  Some  porous  solids 
have  the  property  of  absorbing  gases  to  a  great  extent,  a 
given  body  of  the  solid  absorbing  many 
times  its  own  volume  of  the  gas. 

Demonstration.  —  Trim  a  piece  of  charcoal 
about  an  inch  long  so  that  it  will  slip  easily 
into  a  large  test  tube.  Invert  the  tube  and 
fill  it  with  ammonia  gas.  Pour  mercury  into 
a  dish  and  place  the  piece  of  charcoal  on  its 
surface.  Bring  the  test  tube  down  over  the 
charcoal  and  fix  it  in  such  a  position  that  its 
mouth  will  be  a  little  below  the  surface  of 
the  mercury.  In  a  short  time,  the  charcoal 

will  absorb  the  ammonia,  and  the  mercury  will  rise  in  the  tube,  as 

in  Fig.  173. 


FIG.  173 


GASES 


185 


A  most  important  application  of  the  gas-absorbing  property 
of  charcoal  has  been  made  in  the  construction  of  gas  masks 
to  absorb  poisonous  gases.  The  degree  to  which  the  ab- 
sorption is  carried  depends  largely  upon  the  character  of  the 
charcoal  used.  This  is  determined  not  only  by  the  material 
from  which  the  charcoal  is  made,  but  also  by  the  process  of 
mariufacture.  Charcoal  made  from  coconut  shell  and  peach 
stones  is  of  high  absorptive  quality  and  is  capable  of  being 
broken  into  small  pieces, 
thus  increasing  its  sur- 
face, without  crumbling 
into  dust. 

The  charcoal,  with 
soda,  lime,  and  cement 
granules,'  is  placed  in  an 
absorbing  chamber  or 
canister  and  moistened 
with  a  suitable  chemical 
solution,  sodium  hypo- 
sulphite, for  example, 
for  the  absorption  of 
chlorine. 

While  primarily  made 
for  the  protection  of 
soldiers  in  war,  the  gas  FIG.  174.  — Gas  Mask 

mask  has  many  uses  in 

times  of  peace,  such  as  protection  against  noxious  gases  in 
coal  mines. 

The  mask  shown  in  Fig.  174  is  for  protection  against 
ammonia  fumes.  The  air  inhaled  passes  first  through  a 
canister  containing  the  prepared  charcoal.  The  exhaled  air 
is  released  through  a  flutter  valve  in  front  of  the  neck. 


186 


GASES 


186.  Absorption  of  Gases  by  Liquids.  —  Liquids  also  ab- 
sorb gases  more  or  less  freely.  The  bubbles  of  air  rising 
from  a  glass  of  water  when  it  is  placed  under  the  receiver 
of  an  air  pump  and  the  air  is  exhausted,  afford  evidence 
that  air  is  absorbed  by  water.  It  is  on  account  of  the  ab- 
sorbed air  that  fish  are  able  to  live  in  water.  Water  at  nor- 
mal pressure  and  temperature  absorbs  nearly  twice  its  vol- 
ume of  carbon  dioxide  and  more  than  a 
thousand  times  its  volume  of  ammonia 
gas. 

Demonstration.  —  Fit  two  flasks  with  rubber 
stoppers,  one  having  two  holes  and  the  other 
one  (Fig.  175).  Draw  out  a  glass  tube  to  a 
jet  and  thrust  it  into  the  upper  flask  A  after 
having  filled  A  with  ammonia  gas.  Thrust  two 
tubes  of  the  forms  shown  in  the  figure  through 
the  other  stopper.  Fill  the  lower  flask  B 
nearly  full  with  a  solution  of  litmus  reddened 
with  a  few  drops  of  acid.  Press  in  the  stopper 
and  connect  the  two  straight  tubes  with  a  short 
piece  of  rubber  tubing  having  a  clamp  at  C. 
Loosen  C  and  force  a  little  water  into  A  by 
blowing  through  the  pipe  D,  and  the  water  will 
continue  to  flow  until  the  flask  A  is  nearly  full. 
The  quantity  of  water  that  goes  into  A  will 
measure  roughly  the  gas  absorbed.  Notice  the  change  in  the  color 
of  the  water  in  A.  What  proof  is  there  that  there  was  not  a 
vacuum  in  the  upper  flask? 

The  escape  of  bubbles  from  water  under  the  receiver  of  an 
air  pump  not  only  proves  the  existence  of  the  absorbed  air, 
but  also  proves  that  the  amount  absorbed  depends  upon  the 
pressure.  This  fact  is  made  use  of  in  charging  a  soda  foun- 
tain. This  is  done  by  letting  a  quantity  of  carbon  dioxide 
flow  from  a  high-pressure  tank  into  a  cylinder  partly  filled 


FIG.  175 


GASES 


187 


with  water,  and  rocking  the  cylinder  vigorously  until  the  gas 
is  absorbed.  The  large  amount  of  gas  absorbed  under 
pressure  is  shown  by  the  effervescence  of  the  water  when 
it  is  drawn  out  into  a  glass. 

187.  Diffusion  of  Gases.  —  If  a  closed  vessel  containing 
a  gas  is  connected  with  another  containing  any  different 
gas,  no  matter  what  its  density,  the  gases  will  diffuse  com- 
pletely. 

Demonstration.  —  Fit  a  large  rubber  stopper  with  one  hole  into 
the  open  end  of  a  porous  cup,  such  as  is  used  in  small  battery  jars. 
Put  one  end  of  a  glass  tube  about  2  ft.  long  through 
the  stopper,  and  hold  the  tube  inverted  with  the 
open  end  below  the  surface  of  water  in  a  dish. 
Bring  over  the  porous  cup  a  jar  filled  with  hydrogen, 
or  with  common  illuminating  gas,  and  bubbles  will 
be  seen  to  rush  from  the  end  of  the  tube  and  rise 
through  the  water,  showing  that  gas  has  passed 
into  the  cup.  After  the  bubbles  stop  rising,  remove 
the  jar  and  notice  what  follows. 

It  has  been  proved  that  a  given  volume  of 
a  gas  contains  the  same  number  of  molecules 
as  the  same  volume  of  any  other  gas  at  the 
same  pressure  and  temperature,  and  hence 
that  the  molecules  of  a  light  gas  have  a  greater 
velocity  than  those  of  a  heavy  gas.  Since  the 
velocity  of  the  molecules  of  the  gas  in  the 
outer  jar  is  much  higher  than  that  of  the  air  molecules  in  the 
inner  cup,  the  number  that  strike  the  outside  of  the  porous 
cup  is  correspondingly  greater  than  the  number  that  strike 
the  inside.  This  means  that  a  greater  number  will  pass 
through  the  pores  of  the  cup  from  the  outside  to  the  inside 
than  in  the  opposite  direction,  hence  the  excess  has  to  pass 


FIG.  176 


188 


GASES 


out  of  the  lower  end  of  the  tube.  As  the  number  of  gas 
molecules  increases  within  the  cup,  the  number  of  impacts  on 
the  inside  finally  becomes  equal  to  the  number  on  the  out- 
side, and  no  further  bubbles  will  escape.  When  the  outer 
jar  is  removed,  the  conditions  and  results  are  reversed. 


Questions 

1.  How  does  a  gas  differ  from  a  liquid? 

2.  How  does  the  elasticity  of  a  gas  differ  from  the  elasticity 
of  a  spring  ? 

3.  Why  is  it  possible  to  pump  air  from  a  closed  vessel? 

4.  When  will  an  air  pump  stop  taking  air  from  a  receiver  ?     Is 
it  possible  to  take  it  all  out  ? 

6.  What  will  take  place  if  the  tip  of  an  incandescent  lamp  bulb 
is  broken  off  under  water?    Why? 

6.  Why  does  an  arrow  with  a  cup-shaped  rubber  tip,  stick  to 
the  wall  when  shot  against  it  ? 

7.  To  what  volume  must  a  cubic  foot  of  any  gas  be  compressed 
to  make  its  elastic  force  three  times  as  great  ? 

8.  Why  do  we  not  feel  the  pressure 
of  the  atmosphere  ? 

9.  What   advantage   is    there    in 
having  a  pneumatic  tire  on  an  auto- 
mobile ? 

10.  Why  does  a  deep  sea  fish  look 
bloated  when  brought  to  the  surface? 

11.  Suppose  a  piece  of  rubber  hose 
is    used   to   siphon   water    from   the 
barrel  into  the  pail  (Fig.  177).     Will 
the  water  run  faster  when  the  barrel 
is  full  or  when  nearly  empty  ? 

12.  Suppose    a    hose    is    used    to 
siphon  water  from  a  pit  in  the  side 
of  a  hill,  how  far  below  the  opening 

FIG.  177  of  the  pit  will  it  draw  the  water? 


GASES  189 


Problems 

(The  normal  air  pressure,  when  not  otherwise  given,  is  to  be  reckoned  as 
14.7  Ib.  per  square  inch  or  1033.3  g.  per  square  centimeter.) 

1.  A  rubber  balloon  is  placed  under  the  receiver  of  an  air  pump. 
The  pump  is  worked  until  the  volume  of  the  air  in  the  balloon 
changes  from  128  c.c.  to  352  c.c.     What  is  the  pressure  in  grams 
per  square  centimeter? 

2.  Suppose  the  air  to  be  all  removed  from  an  air-tight  cubical 
box  2  ft.  on  each  edge.     What  would  be  the  pressure  of  the  atmos- 
phere tending  to  crush  the  box? 

3.  A  tank  contains  3.2  cu.  ft.  of  hydrogen  gas  under  a  pressure 
of  275  Ib.  per  square  inch.     If  the  gas  were  allowed  to  expand  until 
the  pressure  was  16  Ib.  per  square  inch,  how  many  cubic  feet  would 
it  occupy? 

4.  To  what  volume  must  a  cubic  foot  of  gas  be  reduced  to  make 
its  elastic  force  five  times  as  great? 

5.  How  deep  must  water  be  in  a  box  so  that  its  pressure  upon 
the  bottom  may  be  the  same  as  that  of  the  atmosphere? 

6.  If  the  box  in  problem  5  were  6  ft.  square,  how  much  would  the 
air  in  it  weigh? 

7.  A  tank  under  a  street  car  has  a  capacity  of  4  cu.  ft.  and  is 
filled  with  air  under  an  atmospheric  pressure  of  15  Ib.  per  sq.  in. 
How  many  additional  cubic  feet  of  air  must  be  forced  into  the  tank 
to  raise  the  pressure  to  90  Ib.  per  square  inch? 

8.  How  many  times  the  volume  of  air  in  an  automobile  tire  at 
an  atmospheric  pressure  of  15  Ib.  per  square  inch  must  be  forced 
into  it  to  have  the  pressure  gauge  read  80  Ib.? 

9.  How  much  excess  of  pressure  is  there  per  square  foot  on  the 
inside  of  a  steam  boiler  over  that  on  the  outside  when  the  pressure 
gauge  (§  179,  6)  reads  73.5  Ib.? 

10.  How  many  foot  pounds  of  work  are  done  by  a  compressed 
air  engine  during  each  stroke,  if  its  piston  is  16  in.  in  diameter,  and 
the  stroke  is  18  in.,  when  the  gauge  shows  an  air  pressure  of  4 
atmospheres? 

11.  To  what  height  would  the  atmospheric  pressure  sustain  a 
water  column  if  the  barometer  reading  is  29.8  in.? 

12.  The  specific  gravity  of  glycerin  being  1,26,  what  will  be  the 


190  GASES 

reading  of  a  glycerin  barometer  when  the  mercury  barometer  reads 
753  mm.?  What  change  in  the  height  of  the  glycerin  column  will 
correspond  to  a  change  of  1  mm.  in  the  mercury  column? 

13.  The  altitude  meter  of  an  airplane  reads  12,000  ft.     What 
should  the  barometer  read  at  that  height  according  to  Fig.  162? 

14.  Pikes  Peak  is  14,108  ft.  high.     According  to  the  graph  in  Fig. 
162,  what  is  the  height  of  the  barometer  at  the  summit  during  fair 
weather?     How  does  the  density  of  the  air  there  compare  with  that 
at  the  level  of  the  sea? 

15.  A  closed  manometer  like  that  in  Fig.  166  is  attached  to  a  tank 
of  compressed  air.     The  air  in  the  manometer  is  reduced  to  one 
fourth  its  original  volume,  and  the  difference  of  level  in  the  mercury 
columns  is  30  cm.     What  is  the  pressure  in  the  tank  in  excess  of 
one  atmosphere? 

16.  The  difference  in  the  height  of  the  two  water  columns  in  an 
open  manometer  is  found  to  be  14  cm.  when  the  manometer  is 
attached  to  a  gas  jet.     By  what  part  of  an  atmosphere  does  the 
pressure  of  the  gas  exceed  that  of  the  air? 

17.  Over  what  height  can  water  be  carried  by  a  siphon  when  the 
barometer  reads  29.1  in.?    What  effect  will  it  have  upon  the  flow 
to  reduce  this  height  to  10  ft.? 

18.  When  the  pressure  on  the  interior  of  an  incandescent  lamp 
sustains  a  column  of  mercury  only  |  mm.  high,  what  is  the  pressure 
in  grams  per  square  centimeter? 

19.  A  diver  is  working  in  30  ft.  of  sea  water,  the  sp.  gr.  of  which 
is  1.025.     What  pressure  must  be  supplied  by  the  compression  pump 
to  counterbalance  the  water  pressure? 

20.  A  force  pump  drives  water  to  a  height  of  156  ft.     What  pres- 
sure in  pounds  per  square  inch  of  surface  must  be  supplied  by  the 
piston? 

21.  A  balloon  contains  500  cubic  meters  of  hydrogen  which  weighs 
90  g.  per  cubic  meter,  and  displaces  505  cubic  meters  of  air.     The 
balloon  covering  and  car  weigh  300  kg.     Each  cubic  meter  of  the 
surrounding  air  weighs  1290  g.    How  many  kilograms  will  the  balloon 
lift  in  addition  to  its  own  weight? 


CHAPTER  VI 


SOUND 

I.    WAVE  MOTION  AND  VELOCITY 

188.  Simple  Harmonic  Motion.  —  If  a  heavy  ball,  sus- 
pended like  a  pendulum,  is  given  a  circular  motion  in  a  hori- 
zontal plane,  the  cord  by  which  it  is  suspended 
will  describe  the  surface  of  a  cone,  and  the  ar- 
rangement is  called  a  conical  pendulum.  To 
an  eye  at  E,  in  the  same  horizontal  plane  as 
that  in  which  the  ball  is  moving,  the  ball  seems 

to    be    moving    in   a 
horizontal    straight 
line,  projected  on  the 
wall  at  AB. 
FlG- 178  Though  the  ball  is 

moving  with  uniform  velocity  around  its  circular  path,  the 
projected  motion  is  a  to-and-fro 
motion,  like  that  of  an  ordinary 
pendulum.  The  velocity  of  this 
projected  motion  is  greatest  at 
the  middle  of  the  path  AB  and 
decreases  to  zero  at  A  or  B. 

If  the  path  of  the  ball  is  repre- 
sented by  the  circle  in  Fig.  179, 
the  corresponding  position  on  the 
line  AB,  at  any  time,  can  be  found 
as  follows,  if  we  assume  that  E  is  at 

191 


192  SOUND 

a  distance  so  great  that  the  lines  EA  and  EB  are  practically 
parallel :  divide  the  circle  into  any  convenient  number  of 
parts,  16,  for  example.  From  the  dividing  points  1,  2,  3,  etc., 
drop  perpendiculars  to  the  line  AB,  meeting  it  at  the  corre- 
sponding points  I',  2',  3',  etc.  Any  body  moving  to  and  fro 
along  the  line  AB  in  such  a  way  that  its  position  at  any  time 
corresponds  to  the  projection  on  A  B  of  a  body  moving  with 
uniform  velocity  around  the  circle  of  reference,  is  said  to 
have  a  simple  harmonic  motion.  It  is  evident  that  the  dis- 
tances l'-2',  2'- 3',  etc.,  are  passed  over  in  equal  times. 

189.  Vibrations  and  Wave  Motion.  —  A  body  or  a  particle 
that  has  simple  harmonic  motion  is  vibrating.  The  great- 
est distance  reached  from  the  position  of  rest  is  the  amplitude 
of  the  vibration.  The  vibration  is  longitudinal  when  this 
motion  has  the  same  direction  as  the  length  of  the  vibrating 
body;  it  is  transverse  when  the  motion  is  perpendicular  to 
the  length. 

When  rapid  vibrations  are  set  up  in  one  part  of  an  elastic 
body,  they  are  transmitted  to  the  other  parts  in  the  form 
of  waves. 

Demonstration.  —  Procure  a  half-inch  spiral  coil  of  spring  brass 
wire  10  or  12  ft.  long,  or  make  one  by  winding  the  wire  on  a  piece  of 


FIG.  180 

gas  pipe  fixed  to  turn  in  a  lathe.  Hook  one  end  of  the  coil  to  a 
screw  hook  in  a  post,  and  taking  the  other  end  in  the  hand,  stretch 
it  somewhat.  Strike  the  coil  a  light,  vertical  blow  near  the  hand, 
and  a  wave  will  run  to  the  fixed  end  and  return  (Fig.  180).  The 
sudden  jerk  felt  by  the  hand  as  the  reflected  wave  strikes  it  shows 
that  the  wave  transmits  the  energy  of  the  blow. 


WAVE   MOTION  AND  VELOCITY  193 

190.   Wave  Length.  —  One  particle  of  a  body  transmitting 
waves  is  in  the  same  phase  as  another  particle  when  it  is  mov- 
ing in  the  same  direc- 
tion   with    the    same 


velocity  at  the  same 
time.  Figure  181 
shows,  the  form  of  a 
wave,  due  to  trans- 

verse vibrations,  moving  from  left  to  right.  The  particle 
A  is  moving  downward  with  a  certain  velocity,  and  the  next 
particle  that  is  in  the  same  phase  is  E.  The  particle  C  has 
the  same  velocity,  but  is  moving  upward.  The  distance  be- 
tween any  particle  and  the  next  particle  in  the  same  phase, 
measured  in  the  direction  of  wave  motion,  as  AE,  is  the 
wave  length.  The  top  of  the  wave  at  B  is  called  the  crest, 
while  the  bottom  at  D  is  the  trough.  The  vertical  distance 
from  B  to  the  horizontal  line  (that  is,  half  the  vertical  dis- 
tance between  B  and  D)  is  the  amplitude.  It  is  a  simple 
matter  to  make  a  body  record  its  own  vibrations  by  tracing 
a  wave  form  similar  to  Fig.  181. 

Demonstration.  —  Bore  a  hole  near  the  end  of  a  long  piece  of 
whalebone,  and  fasten  it  by  a  screw  to  the  side  of  a  block  screwed 
to  a  board.  Rub  a  few  drops  of  kerosene  or  cosmolene  on  one  side 

of  a  strip  of  glass 
so  that  the  surface 
is  evenly  covered 
with  a  thin  layer. 
Put  some  flour  in 
FIG.  182  a  muslin  bag  and 

dust  it  evenly  over 

the  glass.  Place  on  the  board  between  two  guides  and  underneath 
the  whalebone.  Fix  a  bristle  to  the  whalebone  near  the  end  so  that 
it  will  just  touch  the  glass.  Vibrate  the  whalebone,  and  the  bristle 
will  make  in  the  flour  surface  a  nearly  straight  line  twice  the  length 

Rev. 


194  SOUND 

of  the  amplitude.  Vibrate  the  whalebone  again,  and  raise  one  end 
of  the  board  so  that  the  glass  will  slide  out,  and  the  vibrations 
will  trace  a  beautiful  wave  form,  as  shown  in  Fig.  182.  Since  the 
motion  of  the  glass  strip  is  changing,  the  wave  form  is  variable.  If 
the  strip  is  drawn  out  with  uniform  velocity,  the  wave  form  will 
closely  approximate  that  shown  in  Fig.  181. 

191.  Water  Waves  of  small  amplitude  are,  as  a  whole, 
similar  to  those  produced    by   transverse   vibrations  in   a 
stretched  cord.     The  particles  of  the  water,  however,  move 
in  small  circles  or  ellipses,  while  the  wave  moves  onward. 
This  can  be  observed  by  watching  the  motion  of  a  boat  at 
a  distance  from  the  shore ;  the  boat  rises  and  falls  with  the 
waves,  but  does  not  advance  with  them.     Near  the  shore 
the  velocity  of  the  wave  below  the  surface  is  retarded  by  the 
sloping  bottom  and  the  outgoing  water,  so  that  the  top  of 
the  wave  curls  over,  forming  a  breaker,  which  moves  in  the 
direction  of  the  wave. 

192.  Sound  Defined.  —  The  physical  definition  of  sound 
is  any  vibration  that  is  capable  of  being  perceived  by  the 
ear.    The  physiological  definition  includes  also  the  effect 
produced  upon  the  ear  by  such  vibrations. 

193.  A  Sounding  Body  is  a  Vibrating  Body. —  D  emonstrations. 

—  Hold  a  large  jar,  like  the  receiver  of  an  air  pump,  horizontally 

by  the  knob,  and  draw  a  bow  across  the  edge,  or  strike  it  lightly 

with  a  cork  hammer.  Is  it  a  sounding 
body?  Place  a  few  carpet  tacks  inside 
the  jar  near  the  edge.  Repeat  the  ex- 
periment. Is  the  jar  in  vibration? 

Bore  a  hole  in  the  top  of  a  table  and 
firmly  set  into  it  the  handle  of  a  tuning 
FlG  Ig3  fork.     Make  a  cork  hammer  by  thrust- 

ing one  end  of  a  knitting  needle  through 

a  large  cork.    Tie  a  shoe  button  to  the  end  of  .a  fine  silk  thread. 

Strike  one  prong  of  the  fork  with  the  hammer,  and  hold  the  button 


WAVE  MOTION  AND  VELOCITY  195 

on  the  side  of  the  fork  near  the  top.  Do  its  movements  prove 
that  the  fork  is  a  vibrating  body?  Why  does  not  the  button  re- 
bound to  the  same  distance  every  time?  Gradually  lower  it  along 
the  side.  What  is  the  effect?  Hold  the  button  between  the  prongs 
and  observe. 

Both  these  experiments  prove  that  a  sounding  body  is 
in  vibration.  An  interesting  way  to  show  the  vibration  of 
a  tuning  fork  is  to  set  it  in  motion,  and  then  bring  it  in  con- 
tact with  the  surface  of  water  upon  which  lycopodium  powder 
has  been  scattered.  The  rapid  blows  of  the  prong  will  give 
rise  to  a  beautiful  set  of  waves. 

194.  The  Transmission  of  Sound.  —  The  vibrations  of  a 
sounding  body  may  be  transmitted  by  any  elastic  substance. 
Gases,  liquids,  and  most  solids  transmit  sound,  but  with 
varying  intensities  and  velocities. 

(a)  Gases.  —  That  gases  transmit  sound  is  a  matter  of 
universal  experience,  since  the  air  is  the  common  medium 
of  sound  transmission. 

(6)  Liquids.  —  Sound  is  transmitted  by  liquids  more  read- 
ily than  by  gases.  A  person  swimming  under  water  can  hear 
with  great  distinctness  the  sound  of  two  stones  struck  to- 
gether under  the  surface. 

(c)  Solids.  —  A  long  wooden  rod,  a  section  of  gas  pipe, 
or  the  wires  of  a  wire  fence  can  be  used  as  a  means  of  proving 
that  elastic  solids  are  good  conductors  of  sound.  If  an  ob- 
server places  his  ear  at  one  end  of  any  of  these,  while  the  other 
end  is  scratched  with  a  pin,  the  sound  of  the  scratching  is 
plainly  heard  through  the  solid  body,  though  it  may  be  en- 
tirely inaudible  through  the  air. 

195.  Sound  not  Transmitted  in  a  Vacuum.  —  Demonstra- 
tion. —  Fit  a  rubber  stopper  to  an  air  pump  receiver  with  a  small 
neck.       Beside  this  run  two  No.  30  insulated  copper  wires  attached 


196  SOUND 

to  an  electric  bell.  Thrust  the  stopper  in  firmly  to  make  the 
receiver  air-tight.  Exhaust  the  air  so  far  as  possible,  and  ring 
the  bell  by  connecting  the  wires  with  a 
battery.  Notice  that  the  sound  of  the 
bell  is  very  faint.  Slowly  admit  the  air, 
and  notice  how  the  sound  increases  in  in- 
tensity. A  perfect  vacuum  transmits  no 
sound. 

196.  Wave  Motion  in  Air.  —Sound 
is  transmitted  by  means  of  waves, 
but  the  particles  of  air  do  not  vi- 
brate transversely  as  in  the  coil  in 
§  189 ;  they  vibrate  longitudinally— 
that  is,  in  the  same  direction  as  that 
in  which  the  waves  are  moving.  The 
molecules  that  are  put  in  motion  by 

the  first  forward  movement  of  a  sounding  body  are  suddenly 
pushed  ahead  of  it  and  crowded  nearer  together,  forming  a 
condensation;  but 
their  path  is  not 
long,  since  they 
strike  other  mole- 
cules, which  in 
turn  set  the  mole- 
cules next  to  them 
in  motion.  When 
the  sounding  body 
moves  back,  it 
leaves  a  partial 
vacuum,  or  rare- 
faction, behind  it, 
and  into  this  the 

molecules  We   have          FIG.  185.  —  Section  through  Sound  Waves 


WAVE  MOTION  AND  VELOCITY  197 

been  considering  rush  back.  This  sets  up  the  to-and-fro 
motion  of  the  air  that  constitutes  a  sound  wave.  The  con- 
densations and  rarefactions  move  rapidly  outward  in  all 
directions  from  the  sounding  body,  and  follow  in  regular 
succession  as  long  as  the  sounding  body  continues  to  vi- 
brate, at  intervals  that  depend  upon  the  rate  of  the  vi- 
bratron.  In  Fig.  185  the  dark  rings  represent  condensations 
and  the  light  rings  rarefactions  in  a  train  of  sound  waves 
proceeding  from  a  sounding  body  at  the  center. 

Demonstrations.  —  Hook  one  end  of  the  wire  spring  as  before 
(§  189),  and  stretch  the  spring  somewhat  by  pulling  on  the  other  end. 
Put  a  knife  blade  between  two  of  the  turns  of  wire  and  draw  it  toward 
the  end  held  by  the  hand,  pushing  a  few  of  the  coils  together.  Re- 
move the  knife  suddenly,  and  the  wave  will  run  the  length  of  the 
spring  and  be  reflected  by  the  hook  back  to  the  hand.  Tie  a  piece 
of  thread  to  the  spring  at  the  middle,  and  the  longitudinal  vibra- 
tions will  be  shown  by  the  sudden,  jerking,  to-and-fro  motion  of 
the  thread. 

That  a  mechanical  impulse  can  be  sent  through  the  air  as  a  wave 
form  can  be  shown  by  the  use  of  a  tube  8  or  10  ft.  long  and  3  in. 


FIG.  186 

in  diameter.  One  end  of  this  tube  is  capped  with  a  cone  having  an 
opening  an  inch  in  diameter  at  the  small  end,  while  the  other  end 
is  covered  by  a  sheet  of  thin  rubber  tightly  stretched  and  tied  in 
place.  A  short  piece  of  candle  is  lighted  and  so  placed  that  the 
flame  comes  opposite  the  end  of  the  cone.  When  two  wooden  blocks 
are  struck  sharply  together  near  the  closed  end,  the  flame  suddenly 
flares  away  from  the  end  of  the  tube.  The  same  thing  occurs  when 
the  rubber  diaphragm  is  tapped  lightly  with  the  finger.  There  is  no 
passage  of  air  through  the  tube,  for  the  end  is  closed ;  hence  the 


198  SOUND 

movement  of  the  candle  flame  is  the  result  of  the  blow  received 
from  the  condensed  wave  sent  out  by  the  movement  of  the  dia- 
phragm. 

197.  Graphical  Representation  of  a  Sound  Wave.  —  In  a 

sound  wave  the  motion  of  each  particle  of  air  is  either  a  simple 
harmonic  motion  or  a  combination  of  two  or  more  such  mo- 
tions. Though  the  vibration  is  longitudinal,  the  wave 
may  be  represented  by  a  curve  similar  to  that  in  Fig.  181 
if  we  understand  that  all  the  particles  really  move  to  and  fro 
in  the  direction  of  the  horizontal  line,  and  that  the  distances 


5  6  7  '  :2  '.3  v  9 

I     i    i  I  US  I  9   S    '/     S     ff    9  9 


Fig.  187 

A,  particles  at  rest,  when  there  is  no  sound ;  B,  same  particles  at  one  instant  in  a  train 
of  sound  waves;  C,  extent  of  displacement  from  position  of  rest  (not  direction  of 
present  motion)  ;  D,  same  displacements  represented  by  vertical  lines  ;  E,  the  curve 

A,  B,  etc.,  above  this  line  represent  displacements  to  the 
right,  and  C,  D,  etc.,  below  the  line,  displacements  to  the 
left.  Figure  187  illustrates  how  such  a  curve  can  be  drawn. 

198.  The  Velocity  of  Sound  in  Air  has  been  found  directly 
by  taking  the  interval  between  the  time  when  the  flash  of  a 
gun  is  seen,  and  the  instant  when  the  report  is  heard.  The 
distance  between  the  two  stations,  divided  by  the  time  in 
seconds,  gives  the  velocity  per  second. 

If  this  determination  is  made  at  different  seasons,  it  is 
found  that  the  velocity  is  greater  in  summer  than  in  winter. 
At  the  temperature  of  freezing  water,  or  0°  Centigrade, 
the  velocity  of  sound  in  air  is  332.4  m.,  or  1090.5  ft.,  per 


WAVE   MOTION   AND  VELOCITY  199 

second.  The  velocity  at  any  temperature,  in  meters  per 
second,  may  be  found  by  substituting  the  reading  of  the 
Centigrade  thermometer  for  t  in  the  following  formula : 


v  =  332.4  Vl  +  .003665  t.  (41) 

EXAMPLE.  —  Find  the  velocity  of  sound  when  the  thermometer 
roads  26°  Centigrade. 


332.4  Vl  +  .003665  X  26 


=  332.4  Vl.  09529 

=  332.4  X  1.046  =  347.69  meters  per  second. 

If  the  distance  is  -required  in  feet,  it  can  be  found  by  sub- 
stituting 1090.5  for  332.4  in  Formula  41. 

For  approximate  calculations  the  increase  in  velocity 
due  to  a  rise  in  the  temperature  may  be  taken  as  0.6  m. 
or  2  ft.  per  degree  Centigrade,  and  0.33m.  or  1.1  ft.  per  degree 
Fahrenheit.  For  most  purposes  the  approximate  results 
are  sufficiently  accurate. 

199.  The  Velocity  of  Sound  in  Any  Medium  is  directly 
proportional  to  the  square  root  of  the  elasticity  of  the  medium, 
and  inversely  proportional  to  the  square  root  of  its  density. 
By  using  a  proper  numerical  value  for  elasticity  (Formula  1), 
the  velocity  of  sound  can  be  calculated  from  the  equation 

,  =  Velastidty.  (42) 

density 

The  velocity  of  sound  in  air  is  increased  by  a  rise  in  tem- 
perature, chiefly  because  heat  causes  air  to  expand,  and 
thus  decreases  its  density. 

200.  The  Velocity  of  Sound  in  Liquids  varies  according  to 
the  above  law.     The  velocity  of  sound  in  water  has  been 
measured  directly  in  much  the  same  way  as  the  velocity  in 


200  SOUND 

air.  A  bell  was  struck  under  water  in  the  Lake  of  Geneva, 
and  a  quantity  of  powder  was  fired  at  the  same  instant. 
An  observer,  at  a  station  8  miles  away,  measured  the 
time  that  elapsed  between  the  flash  and  the  instant  when 
the  sound  of  the  bell  was  received  through  the  water. 
The  velocity  was  found  to  be  4.3  times  the  velocity  in  air. 
Not  only  is  the  velocity  greater  in  water  than  in  air,  but 
sounds  are  transmitted  more  distinctly.  This  fact  is  made 
use  of  by  submarine  boats  in  communicating  with  ships 
and  other  submarines,  by  under-water  signals. 

201.  The  Velocity  of  Sound  in  Solids  is  so  great  that  in 
measuring  it  directly  the  stations  must  be  far  apart.     Meas- 
urements have  been  made,  however,  and  the  velocity  in 
copper  has  been  found  to  be  about  11.1  times  as  great  as  in 
air,  and  in  steel  wire  15  times  as  great. 

If  the  ear  is  placed  close  to  a  long  wire,  or  to  a  rail  of  a 
railroad,  a  blow  struck  upon  the  wire  or  rail  at  a  distance  will 
be  heard  twice,  first  through  the  solid,  and  then  again 
through  the  air. 

202.  The  Reflection  of  Sound.  —  In  the  first  demonstra- 
tion in  §  196  the  longitudinal  wave  sent  along  the  spring  is 
reflected  from  the  fixed  end.     Sound  vibrations  are  reflected 
in  a  similar  manner.     The  law  of  reflected  motion  (§  65) 
holds  true  for  reflected  sound.     A  good  illustration  of  re- 
flected sound  is  obtained  by  standing  in  a  circular  archway 
with  the  head  in  the  center  of  curvature  of  the  arch,  and 
making  a  slight  hissing  sound.     The  sound  will  be  reflected 
to  the  ear  from  all  points  of  the  arch  and  will  be  much  in- 
creased in  volume. 

203.  Echoes.  —  The  repetition  of  a  sound  through  reflec- 
tion from  any  surface  is  called  an  echo.     The  distinctness 


WAVE  MOTION  AND  VELOCITY  201 

of  the  echo  depends  upon  how  fully  the  sound  is  reflected, 
while  the  length  of  the  sound  that  can  be  repeated  depends 
upon  the  distance  of  the  reflecting  surface.  If  it  takes  one 
second  to  pronounce  a  word,  and  if  the  speaker  hears  the 
echo  as  soon  as  the  word  is  pronounced,  his  distance  from 
the  reflecting  surface  is  about  166.2  m.  (one  half  of  332.4  m.), 
since  in  that  case  the  sound  must  go  from  the  speaker  to  the 
reflecting  surface  and  back  in  one  second.  If  a  single 
syllable  is  pronounced  in  one  fifth  of  a  second,  the  surface 
must  be  at  least  33.24  m.  away  to  produce  a  distinct  echo. 
There  are  several  noted  examples  of  echoes  in  the  hall 
underneath  the  dome  of  the  capitol  in  Washington. 

204.  Multiple  Echoes.  —  When  a  sound  is  made  between 
two  parallel  cliffs,  the  echo  may  be  repeated  many  times, 
thus  forming  a  multiple  echo.  Two  stones  sharply  struck 
together  between  two  parallel  buildings  will  produce  a 
rattling  sound  like  hail,  if  the  buildings  are  the  right  distance 
apart  (about  50  feet).  A  cornet,  sounded  in  a  deep  valley 
between  steep  hills,  will  give  rise  to  a  series  of  musical  echoes 
that  gradually  decrease  in  intensity  and  finally  cease. 

Questions 

1.  What  is  a  simple  harmonic  motion? 

2.  What  is  the  difference  between  a  longitudinal  and  a  trans- 
verse vibration? 

3.  Define  wave  length. 

4.  Is  every  vibrating  body  a  sounding  body  ?    Explain. 

6.  Why  is  sound  carried  more  rapidly  by  solids  than  by  gases? 

6.  Why  does  sound  travel  in  air  more  rapidly  when  the  tem- 
perature rises  ? 

7.  When  the  wind  blows  over  a  field  of  grain  a  series  of  waves  is 
set  up.     Describe  the  motion  of  the  waves  and  of  the  heads  of  grain. 

8.  What  would  be  the  wave  length  in  Fig.  187  if  the  distance 
between  particles  1  and  7  were  8  ft.  ? 


202  SOUND 

9.  Let  L  =  the  wave  length  of  a  given  sound,  N  the  number  of 
vibrations  per  second,  and  v  the  velocity  per  second.  Write  three 
equations,  giving  the  value  of  each  element  in  terms  of  the  other  two. 

10.  How  do  fishes  hear? 

11.  Why  is  it  sometimes  difficult  for  a  good  speaker  to  be  heard 
in  a  public  hall  ? 

12.  How  may  the  difficulty  be  partially  removed? 

Problems 

1.  What  is  the  velocity  of  sound  in  air  when  the  temperature 
is  23°  C.? 

2.  How  great  a  distance  will  the  sound  of  a  whistle  go  in  3 
seconds  when  the  temperature  is  20°  C.  ? 

3.  A  man  is  seen  chopping  wood  and  the  sound  of  the  blow  is 
heard  one  half  second  after  the  ax  is  seen  to  strike.     How  far  away 
is  the  wood  chopper  if  .the  temperature  is  14°  C.  ? 

4.  A  mail  tube  in  a  certain  city  became  clogged  and  a  pistol 
was  fired  at  the  open  end  of  the  tube.     The  report  came  back  from 
the  obstruction  If  seconds   afterward.      How  far  from   the  open 
end  was  the  pipe  stopped,  the  temperature  being  18°  C.  ? 

5.  How  long  after  a  blast  is  set  off  in  a  quarry  will  the  report 
be  heard  at  a  point  8500  ft.  distant,  the  temperature  being  22°  C.  ? 

6.  The  smoke  from  an  exploding  bomb  used  in  day  fireworks 
was  observed,  and  after  an  interval  of  9.4  seconds  the  report  was 
heard.     What  was  the  distance,  the  temperature  being  24°  C.  ? 

7.  Five  seconds  elapsed  between  the  firing  of  a  gun  and  its  echo 
from  a  cliff.     What  was  the  distance  of  the  cliff,  the  thermometer 
reading  20°  C.? 

8.  A  blow,  struck  with  a  hammer  on  the  rail  of  a  railroad,  was 
heard  through  the  rail  in  one  fifth  of  a  second,  and  then  through  the 
air  2.8  seconds  later.     The  temperature  was  18°  C.     How  far  away 
Was  the  blow  struck  ?    What  was  the  velocity  of  sound' in  the  rail  ? 

9.  The  report  of  the  explosion  of  a  submarine  mine  10  miles 
away  was  heard  through  the  water  in  11  seconds.    How  many  times 
greater  was  the  velocity  in  the  water  than  that  in  the  air  at  12°  C.  ? 

10.  Thunder  is  heard  just  11  seconds  after  the  lightning  flash 
is  seen.    The  temperature  being  23°  C.,  what  was  the  distance? 


INTERFERENCE,  RESONANCE,  AND   MUSIC     203 


II.     INTERFERENCE,   RESONANCE,   AND   MUSIC 

205.  Interference  in  Wave  Motion.  —  Demonstration.  — Re- 
peat the  demonstration  of  §  189,  showing  a  transverse  wave  set  up 
in  a  wire  spring  by  a  light  blow.  Just  when  the  wave  is  reflected 
from  the  fixed  end  of  the  coil,  strike  a  second  blow :  the  direct  and 
reflected  waves  will  meet,  and  there  will  be  some  one  part  of  the 
spring  where  the  tendency  of  one  wave  to  raise  the  spring  will  be 
exactly  balanced  by  the  tendency  of  the  other  wave  to  lower  it. 

This  effect  is  called  interference.  Interference  is  a  phe- 
nomenon attendant  upon  all  wave  motion,  and  arises  from 
the  fact  that  a  medium  that  will  transmit  one  wave  motion 
will  also  transmit  others  at  the  same  time.  If  the  resultant 
of  all  the  forces  acting  upon  a  particle  at  any 
time  is  zero,  the  result  will  be  no  motion,  or 
interference.  Interference  in  sound  waves 
produces  silence. 

Demonstration.  — Sound  a  tuning  fork,  — pref- 
erably one  with  a  sounding  box,  as  in  Fig.  188,  — 
and  move  it  rapidly  toward,  and  then  away  from,          FlG- 188 
a  smooth  wall.      Observe  the  interferences  that  take  place. 

206.  Resonance.  —  When  two  waves 
act  in  the  same  direction  upon  a  parti- 
cle, they  cause  it  to  vibrate  with  greater 
amplitude.  The  resulting  amplitude  is 
the  sum  of  the  amplitudes  of  two  waves. 
Such  an  effect  in  sound  waves  gives  rise 
to  a  reinforcement  of  the  sound,  called 
resonance. 

Demonstration.  —  Fill  a  tall  glass  jar 
nearly  full  of  water,  and  get  a  piece  of  large 
glass  tubing  about  a  foot  long,  or  the  chim- 
ney of  a  student  lamp.  Hold  a  sounding 


FIG.  189 


204 


SOUND 


tuning  fork  over  the  upper  end  of  the  tube,  and  push  the  lower  end 
into  the  water,  as  shown  in  Fig.  189,  until  the  air  in  the  tube  re- 
sponds to  the  tone  of  the  fork  and  strengthens  it. 

207.  Principle  of  the  Resonator.  —  The  tube  in  the  above 
demonstration  is  called  a  resonator.     While  the  prong  A 
is  producing  a  condensation  on  one  side,  it  is  producing  a 
rarefaction  on  the  other.     In  order  that  the  sound  of  the  fork 
may  be  strengthened  by  the  resonator,  it  is  necessary  that 
the  condensation  started  by  the  prong  A  in  its  downward 
vibration  (Fig.   189)  shall  go  to  the  bottom  of  the  tube, 
which  is  the  surface  of  the  water  at  B,  and  be  reflected  to  A 
in  time  to  join  the  condensation  produced  by  A  in  its  upward 
vibration.     If,  instead,  the  distance  AB  is  such  that  the  re- 
flected condensation  meets  a  rarefaction,  the  result  will  be 
interference  instead  of  resonance,  and  the  sound  of  the  fork 
will  be  weakened. 

208.  Relation  of  Velocity,  Number  of  Vibrations,  and  Wave 
Length.  —  When  a  body  is  sounding  continuously,  the  air  be- 


FIG.  190 


tween  it  and  a  person  who  hears  it  is  filled  with  a  continuous 
series  of  waves. 

The  condensations  are  a  wave  length  apart,  consequently 
the  wave  length  may  be  defined  as  the  distance  the  sound 
travels  while  the  vibrating  body  is  making  one  complete 
vibration.  The  number  of  these  waves  that  strike  the 
ear  each  second  will  depend  upon  the  rate  of  vibration  of 
the  sounding  body,  and  the  velocity  of  sound  in  the  air 


INTERFERENCE,   RESONANCE,   AND   MUSIC      205 

will  be  the  product  of  the  wave  length  by  the  number  of  vi- 
brations per  second.  That  is, 

«=  NL.  (43) 

For  example,  if  the  wave  length  is  4  ft.  and  the  vibrating 
body  sends  out  280  waves  per  second,  then  the  front  of  the 
first 'wave  will  be  1120  ft.  away  from  the  sounding  body 
when  the  280th  vibration  is  finished. 

209.  Measurement  of  the  Velocity  of  Sound  by  a  Reso- 
nance Tube.  —  It  is  possible  to  compute  the  velocity  of  sound 
in  air  by  measuring  the 
length  of  the  air  column 
in  the  resonance  tube,  and 
combining  this  properly 
with  the  number  of  vibra- 
tions per  second.  A  con- 
venient form  of  tube  and 
support  for  this  measure- 
ment is  shown  in  Fig.  191. 
The  glass  tube  A  is  con- 
nected by  a  flexible  rubber 
tube  to  a  similar  glass  tube 
fastened  to  the  movable 
wooden  arm  B.  This  arm  FlG- 191 

moves  with  so  much  friction  that  it  will  stay  in  any  po- 
sition. The  support  for  the  tuning  fork  is  so  arranged 
that  forks  of  various  lengths  may  be  held  in  position.  By 
pouring  water  into  the  tube  and  moving  B  toward  or  from 
the  vertical  position,  the  length  of  the  air  column  in  A  can 
be  so  fixed  that  it  will  give  a  maximum  reinforcement  to  the 
sound  of  the  fork.  When  this  is  carefully  determined,  the 
length  of  the  air  column  can  be  read  on  the  millimeter  scale 


206  SOUND 

back  of  Ay  which  is  graduated  from  the  position  of  the  fork  as 
zero.  To  find  the  velocity  of  sound  from  this  measurement 
it  must  be  remembered  that  since  the  pulse  of  air  first  given 
out  .by  the  fork  must  go  to  the  bottom  of  the  tube  and 
back,  that  is,  twice  the  length  of  the  tube,  while  the  fork  is 
making  half  of  a  complete  vibration,  it  will  go  four  times 
that  length  while  the  fork  is  making  a  complete  vibration. 
This  means  that  the  wave  length  of  the  fork  is  4  times  the 
length  of  the  air  column.  Calling  the  length  of  the  air  column 
/  and  substituting  the  value  4  I  in  Formula  43,  we  have  v  — 
4  IN.  Experiments  with  tubes  of  different  diameters,  how- 
ever, show  that  a  correction  must  be  made  for  the  diameter  ; 
that  is,  in  order  to  get  correct  results  a  certain  fraction  of  the 
diameter  must  be  added  to  the  length  of  the  air  column  to 
give  one  fourth  of  the  actual  wave  length.  Lord  Rayleigh 
finds  this  fraction  to  be  nearly  four  tenths  the  diameter. 
Including  this  correction  in  the  formula,  we  have 

v=  4N(l  +  OAd).  (44) 


210.  Sympathetic    Vibrations.  —  Whenever    a    sounding 
body  is  near  another  that  has  the  same  time  of  vibration,  it  is 

found  that  the  pulses 
of  air  sent  out  by  the 
first  will  put  the  sec- 
ond in  motion. 

Demonstration.  —  Se- 
~77    "  lect  two  tuning  forks  that 

are  mounted  upon  reso- 

nance boxes,  and  that  give  the  same  number  of  vibrations  per 
second.  Place  them  parallel  to  each  other  at  opposite  ends  of  a 
table,  and  put  one  of  them  in  vibration  with  a  heavy  bow.  Stop 
its  vibrations  with  the  fingers,  after  a  few  seconds,  and  the  second 
fork  will  be  heard.  Its  vibration  may  also  be  shown  by  sus- 


INTERFERENCE,   RESONANCE,  AND  MUSIC      207 

pending  a  light  ball  by  a  thread  so  that  it  will  just  touch  one 
side  of  the  fork. 

The  minute  and  rapid  blows  of  the  condensed  waves  of 
air  striking  upon  the  fork  have  enough  energy  to  set  it  in 
motion,  provided  that  the  rate  of  the  blows  is  the  same  as 
that  of  the  vibrations.  That  this  is  also  the  case  with  a 
heavy  swinging  body  may  be  shown  as  follows : 

Demonstration.  —  Suspend  from  a  hook  in  the  ceiling  a  20-pound 
weight,  and  find  the  time  in  which  it  will  vibrate  as  a  pendulum. 
Strike  the  weight  light  blows  with  a  cork  hammer,  when  it  is  at 
rest,  timing  the  blows  to  the  same  rate  as  that  in  which  it  vibrated. 
If  the  blows  are  given  at  the  right  times,  the  result  will  be  to  set 
the  pendulum  swinging. 

211.  Forced  Vibrations.  —  Demonstrations.  —  Hold  a  toy 
music  box  in  the  hand  and  play  it.  Place  it  upon  a  table  and 
play  it.  Hold  it  against  the  glass  door  of  a  bookcase  and  play  it. 
Describe  the  differences  in  the  effects. 

When  the  music  box  is  played  upon  the  table,  there  is  a 
greater  volume  of  sound  because  the  vibrations  of  the  box 
are  communicated  to  the  table  top  and  put  it  in  motion 
although  their  rates  of  vibration  are  different. 

Since  all  the  tones  played  are  increased  in  volume,  it  is 
evident  that  certain  parts  of  the  table  were  forced  to  vibrate 
in  time  with  the  tones  given  by  the  box.  If  the  end  of  a 
vibrating  tuning  fork  is  pressed  upon  a  table,  the  sound  will 
increase  in  volume  but  will  soon  die  out,  showing  that  the 
energy  of  the  fork  is  rapidly  used  up  in  making  the  table 
vibrate. 

A  thin  tone  is  produced  by  any  vibrating  body  that  puts 
only  a  small  quantity  of  air  in  motion.  Fullness  of  tone  can 
be  secured  only  by  putting  a  large  mass  of  air  in  motion. 
For  this  reason,  in  all  stringed  instruments,  as  the  violin, 


Section  of  a  sound  wave  from  an  electric      Sound  wave  reflected  from  a  concave  cy- 
spark  lindrical  reflector 


Sound  wave  reflected  by  an  elliptical  mir-      Sound  wave  reflected  by  an  elliptical  mir- 
ror, first  position  ror,  second  position 


Sound  wave  reflected  by  an  elliptical  mir-      Sound  wave  reflected  by  an  elliptical  mir- 
ror, third  position  ror,  fourth  position 

Fia.  193.  —  Photographs  of  cylindrical  sound  waves  made  by  Professor 
Arthur  L.  Foley  and  Mr.  W.  H.  Souder,  Indiana  University.  The  source 
of  sound  was  an  electric  spark,  directly  behind  the  black  center  and 
perpendicular  to  the  page.  Used  by  permission.  (p.  208) 


INTERFERENCE,   RESONANCE,  AND   MUSIC      209 

the  guitar,  and  the  piano,  the  strings  are  fastened  to  posts  in 
a  sounding  board  or  wooden  resonator  box. 

212.  Beats.  —  When  two  sounding  bodies  that  have  nearly 
the  same  time  of  vibration  are  sounded  together,  the  alternate 
interference  and  coincidence  of  the  sound  waves  produce 
rhythmical  variations  in  the  intensity  of  the  sound.  These 
are  called  beats  and  can  be  readily  heard. 

If  the  waves  sent  out  by  the  two  sources  are  represented  by  the 
curves  in  the  upper  part  of  Fig.  194,  we  can  see  that  one  body  must 
vibrate  ten  times  while  the  other  vibrates  eleven.  This  means 


FIG.  194 

that  at  every  tenth  wave  of  one,  and  every  eleventh  wave  of  the 
other,  the  waves  will  interfere,  while  at  times  midway  between  the 
waves  will  assist  each  other.  The  curve  resulting  from  these  two 
sets  of  waves  is  shown  in  the  heavy  line.  The  beat  would  come 
between  F  and  G,  at  that  part  of  the  curve  which  swings  the  greatest 
distance  from  the  straight  line  A  B,  while  at  A  or  B,  where  the  in- 
terference is  nearly  complete,  there  would  be  very  little  sound. 
The  heavy  curve  is  constructed  as  follows:  draw  a  set  of  vertical 
lines  across  the  straight  line  AB'}  then  any  point  e  on  the  curve 
will  be  found  by  making  de  equal  to  the  sum  or  difference  of  ah  and 
ac,  depending  upon  whether  they  are  upon  the  same  or  opposite 
sides  of  A  B.  It  is  evident  that  in  order  to  make  a  curve  that  will 
represent  several  beats  between  two  musical  sounds,  a  much  more 
extended  drawing  would  be  required. 

If  two  tuning  forks,  giving  128  and    129  vibrations  per 
second  respectively,  are  sounded  together,  they  will  be  in 

Rev. 


210  SOUND 

the  same  phase  once  per  second  .and  in  opposite  phases  a 
half  second  later.  This  combination  gives  one  beat  per 
second.  If  a  fork  giving  130  vibrations  is  sounded  with  the 
one  giving  128,  they  will  be  in  the  same  phase  twice  per  second 
and  in  .opposite  phases  a  quarter  second  later,  and  there  will 
be  two  beats  per  second.  By  vibrating  together  forks  with 
greater  differences  in  the  number  of  their  vibrations,  it  is 
seen  that  the  number  of  beats  between  two  sounds  is  equal 
to  the  difference  between  the  numbers  of  their  vibrations  per 
second.  This  can  be  demonstrated  by  the  use  of  two  forks 
that  vibrate  in  the  same  time.  By  pressing  a  piece  of  bees- 
wax upon  one  prong  of  one  of  these  forks,  it  can  be  made  to 
give  fewer  vibrations,  and  a  beat  will  be  heard  when  the  forks 
areb  sounded  together.  By  increasing  the  load,  pressing  a 
shot  into  the  wax  if  needed,  a  greater  number  of  beats  per 
second  will  be  produced. 

213.  Properties  of  Musical  Tones.  —  In  order  that  a  vi- 
brating body  may  produce  a  musical  tone,  its  vibrations  must 
be   rapid,    continuous,    and   isochronous.      A   musical   tone 
may  be  a  simple  tone,  in  which  the  vibrations  are  all  alike, 
or  it  may  be  a  compound  tone,  formed  of  a  combination  of 
two  or  more  vibrations.     A  noise  differs  from  a  musical  tone 
in  being  formed  by  a  mixture  of  a  great  variety  of  vibrations 
that  cannot  be  resolved  into  simple  ones.     A  tuning  fork 
gives  a    simple  tone ;    a  piano  string,  a  compound  tone ; 
and  the  fall  of  a  pile  of  lumber,  a  noise. 

The   principal   characteristics  of  musical   tones  are  in- 
tensity, pitch,  and  quality. 

214.  Intensity.  —  The  intensity  of  a  sound  depends  upon 
three  things  :  the  amplitude  of  the  vibration  producing  it,  the 
area,  and  the  distance  at  which  the  sound  is  heard. 


INTERFERENCE,   RESONANCE,  AND  MUSIC      211 

(a)  Amplitude.  —  When  a  tuning  fork  is  struck,  the  energy 
which  it  can  impart  to  the  air  will  depend  upon  the  extent  of 
its  vibrations.  If  these  are  slight,  only  a  weak  tone  is  pro- 
duced. Strike  a  harder  blow,  and  the  amplitude  increases, 
the  energy  the  fork  can  give  to  the  air  is  greater,  and  the 
sound  is  louder.  The  relation  between  amplitude  and  in- 
tensity may  be  readily  shown  by  substituting  a  tuning  fork 
for  the  whalebone  in  the  demonstration  in  §  190.  Make  a 
number  of  traces  on  the  glass  when  the  fork  is  sounding  at 
different  intensities,  and  compare  them. 

(6)  Area.  —  A  small  tuning  fork,  on  being  put  into 
vibration,  sets  only  a  small  quantity  of  air  in  motion  and 
gives  a  sound  having  but  little  intensity;  but  if  the  prongs 
are  broad,  the  amount  of  air  put  in  motion  is  greater  and  the 
sound  is  louder. 

(c)  Distance.  —  Since  the  sounding  body  is  sending  out 
waves  in  every  direction,  the  sound  wave  is  the  outside  of  a 
spherical  shell  of  which  the  body  is  the  center.  The  shell 
of  molecules  to  be  vibrated  becomes  larger  and  larger  as  the 
sound  wave  passes  out  from  the  center,  and  hence  the  energy 
that  can  be  imparted  to  each  air  mole- 
cule becomes  less  and  less.  The  inten- 
sity of  sound  depends  directly  on  the 
amount  of  this  energy. 

Suppose  a  source  of  sound  is  at  the 
point  A,  Fig.  195.     Suppose  this  to  be 
the  center  of  a  spherical  shell  of  which 
the  radius  is  AB :    the  wave  of  sound 
produced  by  the  sounding  body  will  be  received  all  over  the 
surface  of  the  sphere.      If  now  this  sphere  is  replaced  by  a 
larger  one,  of  which  the  radius  is  AC,  the  same  sound  wave 
will  be  received  over  the  larger  surface  and  the  intensity  of 


212  SOUND 

the  sound  on  each  unit  of  area  of  this  surface  will  be 
decreased. 

The  areas  of  these  surfaces  are  directly  proportional  to 
the  squares  of  their  radii ;  hence  we  may  write :  the  in- 
tensity of  sound  varies  inversely  as  the  square  of  its  distance 
from  the  sounding  body. 

If  the  waves  of  sound  can  be  kept  in  one  direction,  as 
by  being  reflected  from  the  inner  surface  of  a  tube,  the  in- 
tensity at  any  point  will  be  greater  and  they  will  go  much 
farther.  Speaking  tubes  are  made  on  this  principle. 

215.  Pitch.  —  The  pitch  of  a  tone  depends  upon  the  number 
of  vibrations  made  per  second  by  the  vibrating  body  that  pro- 
duces it,  the  pitch  being  relatively  high  when  the  vibrations 
are  rapid,  and  low  when  they  are  slow. 

Since  the  velocity  of  sound  is  the  product  of  the  wave 
length  and  the  number  of  vibrations  per  second,  it  is  evident 
that  the  wave  length  is  greater  for  tones  of  a  low  pitch 
than  for  those  of  a  high  pitch.  It  is  also  evident  that  as  the 
period  (or  length  of  time  of  one  vibration)  becomes  greater 
the  pitch  becomes  lower. 

When  the  corner  of  a  stiff  f»ard  is  drawn  across  the  cover 
of  a  cloth-covered  book,  a  certain  sound  will  be  heard.  On 
moving  the  card  more  rapidly,  the  pitch  of  the  sound  pro- 
duced is  made  higher  than  at  first. 

The  speed  at  which  a  circular  or  "  buzz  "  saw  is  running  can 
be  judged  by  the  pitch  of  the  tone  which  it  gives  when  sawing 
a  log.  A  knot  in  the  log  lessens  the  speed  and  lowers  the 
pitch  of  the  tone. 

216.  The  Siren.  —  The  name  siren  is  given  to  an  instrument 
used  to  determine  the  number  of  vibrations  required  to 
produce  tones  of  different  pitch,  as  well  as  to  show  the  re- 


INTERFERENCE,  RESONANCE,  AND  MUSIC     213 

lation  between  them.     A  simple  form  and  the  method  of  us- 
ing it  are  described  in  the  following  : 

Demonstration.  —  Cut  out  a  disk  of  bristol  board,  or,  better,  of 
some  thin  metal,  30  cm.  in  diameter.  From  the  center  describe  four 
concentric  circles,  with  diameters  of  28, 
24,  20,  and  16  cm.  respectively.  Divide 
these  circles  into  32,  24,  20,  and  16  parts 
respectively,  and  drill  holes  6  mm.  in  di- 
ameter through  the  disk  at  these  points. 

Fit  the  disk  to  a  rotating  machine. 
Into  each  end  of  a  rubber  tube  fit  a  glass 
tube ;  and  holding  one  end  directly  op- 
posite to  one  row  of  holes,  put  the  disk  in 
rotation  and  blow  through  the  tube.  If 
the  rotation  is  begun  very  slowly,  the 
separate  puffs  of  air  can  be  heard  as 
they  go  through  the  holes  in  the  disk 
and  are  then  cut  off ;  but  if  the  speed 
is  increased,  the  puffs  will  link  them- 
selves into  a  musical  tone  and  the  pitch 
will  continue  to  rise  as  long  as  the  speed  {  ^L9^' 

is  increased. 

.  .  FIG.  196. — Siren 

Kotate  the  wheel  with  uniform  ve- 
locity and  blow  through  the  holes  in  the  different  circles,  beginning 
with  the  smallest  and  going  to  the  largest.     Is  the  result  pleasing? 
Describe  it.     Compare  with  the  effect  produced  by  blowing  through 
all  four  at  once. 

A  little  practice  will  enable  one  to  turn  the  handle  of  the  wheel 
uniformly.  By  counting  the  number  of  turns  given  to  the  handle 
per  minute  the  number  of  rotations  of  the  siren  wheel  can  be  found. 
The  product  of  the  number  of  rotations  of  the  siren  wheel  per 
second  by  the  number  of  holes  in  the  circle  used  will  give  the  number 
of  vibrations  per  second  for  the  tone  produced. 

217.  Doppler's  Principle.  —  When  both  the  sounding 
body  and  the  ear  that  hears  the  sound  are  stationary,  the 
number  of  waves  that  strike  the  ear  per  second  is  the  same 


214  SOUND 

as  the  number  sent  out  by  the  vibrating  body ;  but  if  either 
is  moving  from  a  position  of  rest,  either  toward  or  away 
from  the  other,  the  number  of  vibrations  that  reach  the 
ear  per  second,  and  consequently  the  pitch  of  the  tone  heard, 
are  changed. 

If  N  represents  the  number  of  vibrations  of  the  sounding 
body,  L  the  wave  length,  and  d  the  distance  over  which  the 
ear  moves  toward  it  in  one  second,  then  the  number  of  vi- 
brations heard  by  the  ear  will  be  N  +  — ,  and  the  pitch  will 

Li 

be  raised.  The  sounding  body  may  itself  be  moving,  or 
both  it  and  the  ear  may  be  moving.  If  the  distance  between 
the  bodies  is  increasing,  let  d  represent  the  increase  per 

second ;   the  number  of  vibrations  received  will  be  ^V  — j 

L 

and  the  pitch  will  be  lowered.  A  good  example  of  this  effect 
is  noticed  when  two  trains  pass  each  other  while  the  engine 
bells  are  ringing.  A  man  standing  by  the  roadside  notices 
that  the  pitch  of  the  horn  of  an  approaching  automobile  is 
higher  than  it  is  after  the  machine  has  passed. 

218.  The  Musical  Scale.  —  A  tone  with  double  the  number 
of  vibrations  of  another  tone  is  called  the  octave  of  the  other 
(from  Latin  octawis,  meaning  "  eighth  "),  since  it  is  the 
eighth  tone  in  what  is  called  the  diatonic  scale.  The  eight 
tones  in  the  diatonic  scale  have  received  names  and  are 
represented  by  notes  placed  in  certain  positions  with  respect 
to  a  series  of  five  parallel  lines  called  a  staff.  These  names 
and  positions  are  shown  below,  where  a  tone  of  256  vibrations 
per  second  (called  middle  C  or  c')  is  taken  as  the  first  tone 
of  the  scale.  A  tone  and  its  octave  resemble  each  other 
closely,  and  have  the  same  name. 


INTERFERENCE,   RESONANCE,  AND   MUSIC      215 

Staff  and  position 


Number  in  scale 1234          56         78 

Letter  names d      d'    e?      f        gf '     a'        b'      c" 

Syllable  names do      re    mi      fa       sol      la         ti      do 

Relative  number  of  vibrations    .    .  256   288  320  341.3  384   426.6*480  512 

Ratio  of  vibrations ' Iff         f         I        §        ¥      2 

Intervals '                     I      ¥      tt       I       V      I       » 

219.  The  Scale  Extended.  —  The  scale  is  extended  into 
higher  pitches  by  taking  the  do  of  512  vibrations  as  1,  and 
multiplying  this  number  by  the  ratios  of  vibrations.     The 
letter  names  are  c",  d" ,  etc.,  and  the  syllable  names,  do,  re, 
etc.,  as  before.     The  next  octave  below  is  found  by  taking  the 
do  of  256  vibrations  as  2.     Hence  the  do  an  octave  below 
has  128  vibrations,  and  from  this  as  1  the  vibrations  can  be 
determined  for  any  tone.     These  tones  are  called  c,  d,  etc., 
and  do,  re,  etc. 

220.  The  Major  Chord.  —  The  scale  given  in  §  218  is  the 
major  scale  formed  upon  the  major  triad  or  major  chord. 
This  chord  consists  of  any  three  tones,  the  numbers  of  whose 
vibrations  per  second  are  in  the  proportion  of  4,  5,  6.     There 
are  three  major  chords,  a$  follows : 

Tonic  =  c':e':g'   =4:5:6 

Dominant  =  #' :  b' :  d"  =  4  :  5  :  6 

Sub-dominant  =  /' :  a' :  c"  =  4 :  5  :  6. 

The  names  of  the  first  tones  of  these  chords  will  suggest 
the  origin  of  the  name  of  the  Tonic  sol  fa  system  of  musical 
notation.  It  will  also  be  observed  that  these  three  major 
chords  include  all  the  tones  of  the  major  scale. 

221.  Intervals  in  the  Scale,  —  The  series  of  ratios  1,  |, 


216  SOUND 

f,  f ,  etc.,  that  express  the  relative  numbers  of  vibrations 
also  express  the  intervals  between  the  do  and  other  tones 
of  the  scale.  The  most  important  of  these  intervals  in  the 
major  scale  are  the  major  third,  -|,  or  do  to  mi;  the  fifth, 
f,  or  do  to  sol;  and  the  octave,  f ,  or  do  to  do, 

222.  The  Keynote.  —  The  note  which  is  taken  as  the  do 
or  1  of  any  scale  is  its  keynote,  and  the  tone  it  represents 
is  the  key  tone  or  tonic  of  the  scale.  The  scale  already  con- 
sidered has  c'  for  its  keynote  and  is  in  the  key  of  C.  Suppose 
we  form  a  major  scale  with  g'  for  its  keynote  and  compare 
the  numbers  of  vibrations  in  its  various  tones  with  those  in 
the  key  of  C. 

g'  a'  V  c"  d"  e"  f  g' 
Key  of  C  .  .  .  384  426.6  480  512  576  640  682.6  768 
KeyofG  /  .  .  384  432  480  512  576  640  720  768 

We  see  by  this  comparison  that  there  are  two  tones  each 
represented  by  a'  and  f",  which  differ  in  the  number  of  their 
vibrations.  The  interval  for  the  two  a"s  is  432 :  426.6,  or 
81 :  80.  This  is  called  a  comma.  The/"'s  differ  more  widely, 
their  interval  being  135 : 128.  This  is  sometimes  called  a 
semitone.  In  order  to  play  music  accurately  in  the  key  of  G, 
two  tones  that  are  not  found  in  the  key  of  C  would  be  required. 
One  of  these,  the  f  of  the  key  of  G,  is  introduced  approxi- 
mately by  increasing  the  vibrations  of  /"  in  the  key  of  C 
by  multiplying  the  number  by  ff ;  this  new  tone  is  called/" 
sharp  or/"$.  The  number  of  vibrations  for  a'  in  the  key  of  G 
differs  so  little  from  that  of  the  same  tone  in  the  key  of  C,  that 
in  most  instruments  one  tone  serves  for  both. 

Inasmuch  as  any  tone  in  any  scale  may  be  taken  for  a  new 
key  tone,  it  is  evident  that  to  introduce  two  new  tones  for 
every  new  scale  on  such  an  instrument  as  the  piano  would 


INTERFERENCE,   RESONANCE,   AND  MUSIC      217 


make  the  keyboard  so  large  that  it  could  not  be  used  at  all. 
Other  complications  come  in  also  when  the  flat  keys  are  used. 
In  these  (for  instance,  in  the  scale  formed  with  f  as  the  key- 
note) the  new  tone  required  by  the  ratio  of  vibrations  is 
secured  by  lowering  the  number  of  vibrations  of  the  corre- 
sponding tone  by  multiplying  it  by  f  f.  The  resulting  tone  is 
called  the  flat  of  the  first,  as  b  flat  or  6fr.  Between  c'  and  d! 
there  would  be  two  tones,  as  follows :  c',  c'§,  d'\>,  df,  having 
for  their  respective  vibrations,  256,  266.6,  276.5,  288. 

223.  Chromatic  Scale ;  Equal  Temperament.  —  In  practice 
there  is  but  one  key  on  the  piano  between  C  and  D,  and  this 
is  called  either  (7$  or 
J)b.  In  addition  to 
the  eight  tones  of  the 
major  diatonic  scale,  c  \  D  E  F  G  \  A  B  C 

there  are  five  flats  or 
,  ,       „    ,,.  FIG.  197 

sharps,  and  all  thir- 
teen together,  when  played  in  order,  constitute  the  chro- 
matic scale.  The  system  adopted  to  fix  the  number  of 
vibrations  for  each  of  the  thirteen  tones  of  each  octave  on 
the  piano  is  called  the  system  of  equal  temperament.  The 
twelve  intervals  (semitones)  in  the  scale  are  made  equal, 
and  this  interval  is  ^2,  or  1.05946+.  This  means  that  the 
number  of  vibrations  of  any  of  these  thirteen  tones  is  ob- 
tained by  multiplying  the  number  of  vibrations  of  the  pre- 
ceding one  by  1.05946. 

Figure  198  shows  graphically  the  difference  between  the 
equally  tempered  scale  and  the  scale  with  sharps  and  flats 
given  their  true  vibration  numbers,  for  the  octave  beginning 
with  c'  =  256  vibrations  and  extending  to  c"  =  512  vibra- 
tions. A  skilled  violin  player  with  a  well-trained  ear  will 


C 

c8 
D*> 

D 

D$ 

E* 

F$ 

a* 

a 

G« 
A\> 

T 

A 

A* 
BV\ 
B 

E 

F 

218 


SOUND 


play  the  true  intervals  of  the  scale.     This  is  one  reason  why 
the  music  of  a  string  quartet  is  very  pleasing. 


EQUAL 
TEMPERAMENT 


TRUE 
INTERVALS 


G  512.0_T_512.0  C 


JB483.3_ 


A  430.5- 


406.4- 


F  341.7. 


E  322.5  _ 


D  287.3_ 
(7*orDl>271.2_ 


224.  Quality  or  Timbre.  —  When 
we  hear  a  musical  sound,  we  have 
no  difficulty  in  recognizing  the 
kind  of  instrument  that  produces 
it.  The  sound  of  the  violin,  of  the 
piano,  of  the  cornet,  has  each  its 
own  peculiarity.  One  voice  is  full 
and  rich,  another  is  thin,  and  an- 
other is  monotonous.  The  char- 
acteristics which  enable  us  to  assign 
_409.5  A*°  a  sound  to  its  source  are  called  the 
_400.0  #*  quality  of  the  tone.  The  physical 


-480.0  B 

-460.8  B* 

_444.4  A* 


383.6-1-384.0  G 

-368.6  G* 

_  355.5  F* 

341.3  F 


explanation  of  quality  .is  that  most 
sounding  bodies  vibrate  not  only  as 
a  whole,  but  also  in  various  parts, 
as  does  the  string  of  a  piano,  and 
that  a  sound  is  rich  in  quality  when 
it  contains  various  overtones  pro- 
duced by  these  partial  vibrations, 
as  well  as  the  fundamental  tone  of 
the  vibrating  body. 

The  wave  form  of  a  tone  which 
is  rich  in  quality  is  a  complex  one. 
Besides  the  full  length  wave  given 
by  the  fundamental  tone,  there  is 
one  \  as  long,  given  by  the  first 

harmonic,  one  |  as  long,  given  by  the  second  harmonic, 
and  so  on.  For  example  :  If  the  fundamental  is  c',  the 
first  harmonic  is  c",  the  second  is  g",  the  third  is  c'",  etc, 


-320.0  E 

_307.2  jEb 
-300.0  £>* 

-288.0  D 


C  256.0. 
FIG.  198 


-276.5  D* 
_266.6  C* 
256.0  C 


INTERFERENCE,  RESONANCE.  AND  MUSIC      219 

225.  Harmony  and  Discord.  —  Two  musical  sounds  are 
said  to  produce  harmony  when,  on  being  sounded  together, 
they  produce  a  result  pleasing  to  the  ear.  If  the  result  is 
displeasing,  they  are  said  to  produce  discord.  One  cause 
of  discord  is  the  presence  of  beats  between  the  two  tones, 
and  the  greatest  discord,  between  tones  of  medium  pitch, 
results  when  the  beats  are  about  32  per  second ;  if  the 
number  of  beats  is  fewer  than  10  or  greater  than  70  per  second, 
they  are  somewhat  unpleasant  but  do  not  produce  discord. 

Questions 

1.  Under  what  conditions  will  two  wave  motions  completely 
neutralize  each  other?     What  will  be  the  result  if  they  are  water 
waves?    What  if  they  are  sound  waves? 

2.  If  a  tuning  fork  is  put  in  vibration  and  then  rotated  while 
it  is  held  near  the  ear,  there  will  be  four  times  per  rotation  when  it 
can  hardly  be  heard.     Explain. 

3.  If  a  tuning  fork  is  held  over  the  mouth  of  a  resonator,  while 
vibrating,  and  slowly  rotated,  a  point  can  be  found  at  which  there 
is  practically  no  resonance.     When  a  tube  is  slipped  over  the  upper 
prong,  without  touching  it,  the  sound  of  the  resonator  will  again 
be  heard.     Explain. 

4.  Why  cannot  one  fork  be  set  in  motion  by  another  unless 
its  rate  of  vibration  is  the  same? 

6.  Why  do  soldiers  break  step  on  crossing  a  bridge? 

6.  Why  does  an  auto  horn  seem  to  have  a  higher  pitch  before 
you  meet  it  than  after  it  has  passed  ? 

7.  Why  does  the  chord  do,  mi,  sol,  have  a  richer  sound  than 
either  of  the  tones  alone  ? 

8.  How  many  keys  would  it  require  for  an  octave  on  the  piano 
if  the  sharps  and  flats  were  not  played  on  the  same  key? 

9.  Does  a  violin  player  in  a  string  quartet  play  the  equally 
tempered  or  true  interval  scale?     Why? 

10.  Why  does  a  singer  sometimes  prefer  the  piano  accompani- 
ment to  a  song  to  be  played  in  the  key  of  three  flats  instead  of  in 
the  key  of  four  sharps? 


220  SOUND 


Problems 

1.  The  air  column  of  a  resonance  tube  which  gives  the  maxi- 
mum reinforcement  to  the  sound  of  a  tuning  fork  is  12.5  in.     Find 
the  wave  length  of  the  fork.     (A  correction  for  the  diameter  of  the 
tube  need  not  be  made.) 

2.  A  tuning  fork  gives  384  vibrations  per  second.     What  must 
be  the  length  of  a  resonating  tube  for  it  at  a  temperature  of  0°  C.? 

3.  What  is  the  velocity  of  sound,  determined  by  the  apparatus 
shown  in  Fig.  191,  when  the  resonator  tube  is  22  mm.  in  diameter 
and  248.5  mm.  long,  if  the  fork  makes  .320  vibrations  per  second, 
the  temperature  being  0°  C.  ? 

4.  Two  tuning  forks  vibrate  126  and  128  times  per  second  re- 
spectively.    How  many  times  per  second  do  they  reenforce  each 
other? 

6.  Two  tuning  forks  that  give  260  vibrations  per  second  are 
sounded  together,  showing  by  the  absence  of  beats  that  they  are  in 
unison.  One  of  them  is  now  loaded  until  five  beats  are  heard  per 
second.  How  many  vibrations  does  it  now  give? 

6.  Suppose  the  inmost  row  of  holes  in  the  siren  described  in  the 
demonstration  in  §  216  gives  the  tone  c'  =  256  vibrations.     How 
many  times  does  the  disk  rotate  per  second?     What  tones  will  the 
other  rows  of  holes  give  ? 

7.  What  change  in  the  speed  of  the  siren  disk  must  be  made  to 
lower  the  tone  an  octave? 

8.  A  person  in  an  automobile  that  is  being  driven  at  the  rate  of 
25  miles  per  hour  blows  a  whistle  that  gives  320  vibrations  per 
second.     How  many  vibrations  per  second  will  reach  the  ear  of  a 
man  'standing  by  the  roadside,  first,  before,  and  second,  after  it  has 
passed,  if  the  temperature  is  20°  C.  ? 

9.  If  c'  has  256  vibrations,  show  how  to  find  the  number  of 
vibrations  in  d'  and  e'  as  played  on  the  violin ;  on  the  piano. 

10.  Show  why  a  tone  must  be  introduced  into  the  scale  of  the 
key  of  G  that  cannot  be  found  in  the  scale  of  the  key  of  C. 

11.  In  the  time  of  Handel  the  standard  a'  fork  gave  424  vibra- 
tions per  second.     The  present  international  a'  fork  gives  435  vi- 
brations.    What  effect  does  this  have  upon  the  difficulty  of  singing 
the  high  notes  of  a  song  written  by  Handel  ? 


VIBRATION  221 

III.   VIBRATION  OF  STRINGS,  AIR  COLUMNS,  ETC.; 
COMBINATION  OF  VIBRATIONS 

226.  The  Sonometer.  —  To  investigate  the  laws  of  the  vi- 
bration of  strings  an  instrument  called  the  sonometer  is  used. 
This  is  also  called  a  monochord,  since  it  often  has  but  a  single 
string.  The  essential  parts  are  a  base  with  a  bridge  at  each 
end,  a  pin  to  which  to  fasten  one  end  of  the  string,  and  some 
method  of  stretching  the  string  by  attaching  a  spring  balance 


FIG.  199.  — Sonometer  with  Two  Strings 

or  weights  at  the  other  end.  A  movable  bridge  (at  E  in 
Fig.  199)  is  used  to  change  the  length  of  the  vibrating  string, 
and  a  scale  is  laid  off  on  the  base. 

227.  Laws  of  the  Vibration  of  Strings. 

I.  The  tension  and  mass  per  unit  length  being  the  same, 
the  number  of  vibrations  per  second  varies  inversely  as  the  length 
of  the  string. 

II.  The  length  and  tension  being  the  same,  the  number  of 
vibrations  per  second  varies  inversely  as  the  square  root  of  the 
mass  per  unit  length  of  the  string. 

III.  The  length  and  mass  per  unit  length  being  the  same, 
the  number  of  vibrations  per  second  varies  directly  as  the  square 
root  of  the  tension. 

The  above  laws  can  be  expressed  by  the  proportion 

y  T 
N:N'= 


222  SOUND 

For  the  first  law,  under  the  conditions  given,  the  propor- 
tion becomes 

N:N'=-l:j,,  or,  N:Nf  =/':/. 
i    i 

If  the  length  of  a  certain  string  is  taken  as  unity  the  parts 

of  the  same  string  that  give  the  other  tones  of  the  scale  are  as 

follows  : 

Syllable  names  :   do     re    mi    fa    sol    la    ti    do 

Length  of  string:  iff       f       f      f    &     | 

It  will  be  observed  that  these  ratios  which  give  the  relative 

length  of  string  are  the  reciprocals  of  the  ratios  giving  the 

relative  numbers  of  vibrations. 

For  the  second  law  the  proportion  becomes 

N:N'  =—  L:-4=,  or,  N:N'  = 
Vjf  ' 


and  for  the  third  law,  N:N'= 

These  laws  can  be  verified  on  the  sonometer. 

The  strings  of  the  piano  illustrate  the  preceding  laws. 

The  lowest  tones  are  made  by  long,  heavy  strings  without 

great  tension,  while  the  highest  tones  are  made  by  short, 

light  strings  stretched  to  a  high  tension. 

228.    Nodes  and  Loops.  —  Demonstration.  —  Hook  one  end 
of  the  wire  spring  as  in  §  189.     Throw  the  coil  into  vibrations  as  a 


FIG.  200 

whole  by  a  slight  movement  of  the  hand.  Quicken  the  movement, 
and  it  can  be  thrown  into  vibrations  in  halves,  thirds,  quarters,  etc., 
giving  a  number  of  complete  "  stationary  waves." 


VIBRATION  223 

When  the  spring  is  vibrating  as  shown  in  Fig.  200,  the  points 
of  no  vibration  are  called  nodes,  asJV,  N',  while  the  points 
of  maximum  vibration,  as  L,  Lf,  etc.,  are  called  loops.  The 
vibrations  are  caused  by  waves  sent  out  from  A  and  reflected 
from  B.  Whenever  the  wave  starting  from  A  tends  to  give  a 
certain  velocity  to  any  particle,  and  the  reflected  wave  from 
B  tends  to  give  it  an  equal  velocity  in  the  opposite  direction, 
the  two  forces  neutralize  each  other,  the  particle  remains  at 
rest,  and  a  node  is  formed. 

When  the  string  of  a  musical  instrument  is  put  into  vibra- 
tion by  drawing  a  bow  across  it,  by  striking  it  a  blow,  or  by 
plucking  it,  it  vibrates  transversely,  not  only  as  a  whole, 
giving  its  fundamental  tone,  but  also  in  halves,  thirds, 
fourths,  etc.,  each  one  of  which  gives  its  own  tone.  These 
different  tones,  with  the  fundamental,  determine  the  quality 
of  the  tone. 

Demonstration.  —  Place  a  wire,  or  heavy  bass  viol  string  on  the 
sonometer  and  stretch  it  until  it  gives  a  suitable  tone.  Sound  the 
fundamental  tone  with  the  bow.  Touch  the  string  lightly  in  the 
middle  with  the  finger  and  draw  the  bow  across  the  string  one  fourth 
the  length  of  the  string  from  the  end.  This  will  sound  the  octave. 
Touch  the  finger  at  one  third  the  length  of  the  string  from  the  end. 
Draw  the  bow  at  one  sixth  and  the  note  sounded  will  be  the  second 
harmonic,  etc. 

229.  Overtones  and  Harmonics.  —  It  is  not  necessary  to 
touch  the  string  in  order  to  make  it  vibrate  in  parts  besides 
vibrating  as  a  whole.  The  tones  caused  by  the  vibrations 
in  parts  can  be  heard  by  listening  carefully  when  the  string 
is  plucked.  These  tones  are  called  overtones,  and  if  the 
numbers  of  vibrations  which  produce  them  are  2,  3,  4,  etc., 
times  the  number  of  vibrations  of  the  fundamental,  they 
are  called  harmonics.  Overtones  can  be  very  readily  pro- 


224 


SOUND 


FIG.  201 


duced  on  a  guitar  and  form  the  most  ac- 
curate method  of  tuning  it. 

230.  Nodes  and   Loops  in   a   Bell.  - 

Demonstration.  —  Mount  a  bell  jar  as  in  Fig. 
201  and  put  it  in  vibration  by  striking  it  lightly 
with  a  cork  hammer,  or  by  drawing  a  violin 
bow  across  its  edge.  It  will  give  out  a  bell- 
like  tone.  If  the  bow  is  drawn  midway  be- 
tween two  of  the  suspended  balls,  they  will  all 
remain  in  contact  with  the  rim,  showing  the 
existence  of  nodes;  but  if  one  of  the  balls  is 
raised  and  the  bow  drawn  at  the  point  where 
it  rested  upon  the  rim,  the. three  other  balls 
will  be  thrown  into  vibration,  showing  the  position  of  the  loops. 

231.  Vibration  of  Air  Columns.  —  In  most  musi- 
cal instruments  called  wind  instruments,  the  tones 
are  produced  by  the  vibrations  of  columns  of  air, 
of  different  lengths.  There  are  three  classes  of 
mouthpieces,  by  means  of  which  the  air  is  put  into 
vibration  in  wind  instruments. 

In  the  first  class  the  air  is  blown  across  the  sharp 
edge  of  an  opening,  as  in  the  whistle,  the  organ  pipe 
(Fig.  202),  and  the  flute. 

In  the  second  class  the  air  is  blown  past  a  thin,  flat 
tongue  called  a  reed,  which  by  its  vibration  opens  and  closes 

the  opening  into  the  air  column. 
The  striking  reed  (Fig.  203,  A), 
used  in  the  clarinet,  closes  the  open- 
ing by  striking  upon  its  edges ;  the 
free  reed  (Fig.  203,  B),  used  in  the 
accordion  and  reed  organ,  nearly 
closes  the  opening  by  vibrating 
FIG.  203  back  and  forth  through  it. 


FIG.  202 


VIBRATION 


225 


FIG.  204 


.V 


D 


In  the  third  class  of  wind  instruments  the  lips  are  generally 
used  as  vibrating  membranes  through  which  the  air  is  blown 
into  the  instrument.  Figure  204 
shows  the  mouthpiece  of  a  trum- 
pet. 

232.  Nodes  and  Loops  in  an 
Organ  Pipe.  —  The  vibration  of 
air  in  a  tube  is  in  the  direction  of  its  length,  but  it  can  give 
rise  to  nodes  and  loops  as  well  as  a  vibrating  cord. 

In  this  case,  however,  the  node  must  be  understood  to 
mean  a  point  where  the  particles  of  air  remain  at  rest,  but 
where  there  are  rapid  changes  from  condensation  to  rare- 
faction, and  vice  versa.  A  loop  means  a  point  where  there  is 
the  greatest  motion,  but  no  change  of  density.  From  this  it 
will  be  seen  that  the  end  of  a  closed  pipe  must  form  a  node, 

and  the  end  of  an  open  pipe  a 
loop.  In  A  (Fig.  205),  a  node 
would  be  at  the  upper  end  and 
a  loop  at  the  mouth ;  conse- 
quently the  length  of  a  closed 
pipe  is  one  fourth  the  wave 
length  of  its  fundamental  tone, 
as  is  the  case  in  the  resonator 
tube  in  §§  207,  209.  If  the 
pipe  is  blown  strongly,  it  will 
give  out  a  tone  higher  in  pitch, 
but  a  node  will  still  be  at  the  closed  end  and  a  loop  at  the 
mouth.  In  this  case  (B)  there  will  be  an  intermediate  node 
and  loop  at  N'  and  L',  and  the  length  of  the  pipe  will  be 
three  fourths  the  wave  length  of  the  tone  produced. 

In  the  open  pipe,  C  (Fig.  205),  there  will  be  a  loop  at  each 
end,  and  a  node  in  the  middle,  and  the  length  of  the  pipe 

Rev. 


N' 


r 


r/ 


N 


L' 


N' 


i? 


FIG.  205 


226  SOUND 

will  be  half  the  wave  length  of  the  fundamental  tone.  If 
the  next  higher  tone  is  produced,  there  will  be  two  nodes, 
N'  and  N",  and  an  additional  loop  L'  and  the  length  of  the 
pipe  will  be  equal  to  the  wave  length  of  the  tone. 
Comparing  A  and  C  it  will  be  seen  that  the  funda- 
mental tone  given  out  by  an  open  pipe  is  the  oc- 
tave of  the  tone  produced  by  a  closed  pipe  of  the 
same  length. 

Demonstration. — Procure  an  organ  pipe,  one  side  of 
which  is  glass,  and  lower  into  it,  by  a  thread,  a  light  ring 
over  which  is  stretched  a  membrane  with  fine  sand 
sprinkled  over  it,  as  shown  in  Fig.  206.  When  the  fun- 
damental tone  is  sounded  and  the  ring  is  lowered,  the 
sand  will  show  by  its  movements  that  the  amount  of  the 
vibration  is  decreasing  until  the  middle  of  the  tube  is 
reached,  where  it  will  come  to  rest.  Increase  the  force 
of  the  bellows  that  blow  the  pipe,  so  as  to  produce  the 
higher  tone;  the  middle  point  becomes  a  loop,  as  is 
shown  by  the  dancing  of  the  sand. 

If  an  opening  is  made  in  the  side  of  a  pipe, 
this  becomes  a  loop  and  changes  the  pitch  of  the 
tone  produced.  In  this  way  the '  different  tones 

X1  IG«   ^Oo 

of  a  flute  are  made  by  the  fingers  of  the  player 
stopping  and  unstopping  holes  along  the  side. 

233.  The  Vibration  of  Rods  and  Tubes.  —  A  rod  fixed  at 
one  end  may  be  put  in  transverse  vibration  by  being  struck 
or  plucked  at  the  free  end  —  as  in  the  music  box.  The  longer 
the  rod,  the  lower  the  tone  produced. 

Rods  may  be  made  to  vibrate  longitudinally  as  well  as 
transversely. 

Demonstrations.  —  Hold  a  glass  rod,  a  meter  long  or  more,  by 
the  middle  with  one  hand,  while  with  the  other  you  draw  a  moist 


VIBRATION  227 

cloth  lightly  from  the  middle  to  the  end.  The  rod  will  be  thrown 
into  longitudinal  vibrations,  and  the  fundamental  tone  will  be  pro- 
duced. Do  the  same  with  a  wooden  rod,  a  brass  rod,  and  a  brass  tube 
of  the  same  length  and  diameter,  using  a  rosined  cloth  for  a  rubber. 
Does  the  pitch  of  the  tone  depend  upon  the  material  of  the  rod? 

Repeat  the  above  demonstration  with  two  glass  tubes  of  different 
diameters,  but  of  the  same  length.  Does  the  pitch  of  the  tone  de- 
pend upon  the  diameter  of  the  tube?  Repeat  with  one  of  these 
tubes  and  another  of  the  same  diameter  but  only  half  as  long.  Does 
the  pitch  depend  on  the  length  of  the  tube  ?  How  do  the  two  tones 
compare  ? 

The  sound  caused  by  rubbing  the  tubes  and  rods  in  the 
above  demonstrations  is  due  to  longitudinal  vibrations. 
That  such  vibrations  exist  may  be  shown  as  follows : 

Demonstration.  —  Clamp  a  brass  rod  firmly  to  a  block  upon  a 
table  as  shown  in  Fig.  207. 
Suspend  an  elastic  ball  so 
that  it  will  rest  against  one 
end  of  the  rod,  and  then 
draw  a  rosined  cloth  from 
the  middle  to  the  other  end. 
The  longitudinal  vibrations 

will  cause  the  rod -to  give  out  a  high  tone,  and  will  repel  the  ball  from 
the  end  of  the  rod. 

The  mechanical  effect  of  vibrations  in  tubes  is  sometimes 
very  great.  It  is  not  uncommon  for  a  test  tube  to  be  cracked 
into  a  spiral  ribbon  running  from  end  to  end,  on  being  wiped 
with  a  damp  towel.  If  a  glass  bell  jar  is  bowed  vigorously 
a  few  times  with  a  violin  bow,  it  may  be  shattered  even  if 
the  walls  are  a  quarter  of  an  inch  thick. 

234.  The  Vibration  of  Plates.  —  If  a  thin  plate  of  metal 
or  glass  is  clamped  to  a  support  at  the  middle,  and  a  bow 
is  drawn  across  its  edge,  it  will  be  thrown  into  vibration 


228 


SOUND 


and  will  produce  sound.     The  positions  of  the  nodal  lines 
of  the  plate  can  be  shown  very  readily  as  follows : 

Demonstrations.  —  Sift  sand  evenly  over  the  surface  of  a  brass 
plate  fastened  by  the  middle,  as  the  first  one  in  Fig.  208.  Place  a 
finger  at  one  corner  and  draw  a  bow  across  the  middle  of  one  side. 
The  sand  will  be  thrown  violently  about,  and  will  finally  come  to  rest 
on  those  parts  of  the  plate  that  do  not  vibrate,  so  that  the  lines  of 
sand  indicate  the  nodal  lines.  Figure  208  shows  a  number  of  plates 


FIG.  208 

differing  in  form,  size,  and  thickness,  and  a  few  of  the  many  interest- 
ing figures  that  can  be  produced  by  them.  If  the  plates  are  clamped 
by  the  corner  or  at  one  side,  a  new  set  of  figures  will  be  obtained. 

Scatter  a  little  lycopodium  powder  on  the  plate  with  the  sand, 
and  it  will  be  found,  .on  vibrating  the  plate,  that  the  powder  will 
collect  over  the  places  of  greatest  vibration  instead  of  at  the  nodal 
lines  as  the  sand  does.  Examine  carefully  and  explain  why  this 
happens.. 

235.  Graphical  Method  of  Combining  Vibrations.  —  It  is 

frequently  desirable  to  represent  graphically  the  relation 
that  exists  between  the  vibrations  of  tones  of  different  pitches. 
The  method  usually  adopted  is  to  consider  the  vibrations 
of  the  two  bodies  to  be  made  at  right  angles  with  each  other, 
and  to  construct  a  curve  that  shall  be  the  result  of  the  two 
vibrations  combined.  If  the  vibrations  producing  the  tones 
c  and /are  to  be  combined,  the  curve  can  be  made  graphically 
as  follows : 


VIBRATION 


229 


Suppose  a  point  moving  back  and  forth  along  AC,  in  simple 
harmonic  motion  corresponding  to  uniform  motion  around 
circle  //,  to  represent  the  vi- 
brations that  produce  c,  and 
suppose  a  point  moving 
along  AB  in  simple  har- 
monic motion  with  reference 
to  circle  D  to  represent  the 
vibrations  that  produce  / 
(Fig.  209).  Since  the  ratio 
of  the  numbers  of  vibrations 
in  these  two  tones  is  1 :  |, 
the  body  sounding  the  tone 
/  vibrates  eight  times  while 
the  body  sounding  c  vibrates  six  times,  and  therefore  makes 
one  sixth  of  a  vibration  while  the  body  sounding  c  makes  one 
eighth  of  a  vibration.  Lay  off  the  circumference  DEF  into 
six  equal  parts,  and  the  other  circumference  into  eight. 
From  the  points  of  division  draw  lines  perpendicular,  re- 
spectively, to  AB  and  AC,  and  prolong  them;  then  their 
intersections  will  give  the  points  for  the  required  curve.  In 
order  that  the  curve  connecting  the  points  shall  be  smooth, 
intermediate  points  must  be  determined. 

The  curve  representing  the  combination  of  any  other 
two  tones  can  be  constructed  in  the  same  way. 

236.  The  Pendulum  Method  traces  the  curve. 

Demonstration.  —  On  the  opposite  sides  of  a  baseboard,  about 
40  cm.  square,  fasten  two  uprights  102  cm.  long  above  the  upper 
surface  of  the  base.  Fix  a  crosspiece  to  the  top  of  these.  Bore  a 
hole  in  the  middle  of  this  and  fit  a  handle  so  that  it  will  turn  snugly. 
Make  a  lead  disk  10  cm.  in  diameter  and  2  cm.  thick,  and  through 
the  middle  drill  a  hole  5  mm.  in  diameter.  Suspend  this  by  three 


230 


SOUND 


FIG.  210 


cords  as  in  Fig.  210,  and  at  the  point  A  tie  these  three  cords  to  two 
others  which  run  through  the  holes  B  and  C  in  the  crosspiece  and 
then  through  a  hole  in  the  handle  H.  Wind 
a  ring  of  copper  wire  R  about  the  two  cords, 
so  that  it  can  be  slipped  up  or  down,  and 
unite  the  two  into  one,  as  R  A.  Place  a 
glass  plate  on  the  baseboard,  and  sift  sand 
upon  it  from  a  tin  flour  dredge.  Select  a 
glass  rod  or  tube  that  will  slip  easily,  through 
the  hole  in  the  disk,  and  make  one  end  small 
and  rounded  in  a  Bunsen  flame.  Put  the 
rod  through  the  disk ;  then  draw  the  disk 
back  and  release  it  so  that  it  will  vibrate 
across  the  base  in  the  direction  DE.  The 
disk  swings  as  a  pendulum  from  the  points 
C  and  B,  and  the  rod  traces  a  straight 
line  in  the  sand.  Vibrate  again  in  a  direc- 
tion GF,  at  right  angles  to  DE.  The  rod 
will  again  trace  a  straight  line,  swinging  from  the  point  R. 
Now  draw  the  disk  aside  midway  between  these  directions,  and 
when  it  is  released  the  rod  will  trace  a  curve  which  will  be  the  result 
of  combining  the  two  motions,  and  the  form  of  which  will  depend 
upon  the  relative  lengths  of  the  two  pendulums,  i.e.  of  the  points  K 
and  R  from  the  middle  of  the  lead  disk. 

The  distance  of  K  from  the  middle  of  the  disk  can  be  kept  at  1  m. 
by  turning  the  handle  H ;  and  by  making  the  distance  of  R  from  the 
middle  of  the  disk  such  that  the  short  pendulum  vibrates  three  times 
while  the  long  one  vibrates  twice,  the  curve  corresponding  to  the  com- 
bination of  the  tones  sol  and  do  is  obtained.  If  the  times  of  vibration 
are  as  2 :  1,  the  curve  will  represent  the  combination  of  a  tone  and 
its  octave.  By  applying 
the  law  of  the  pendulum  for 
length  and  time  of  vibration, 
the  length  of  the  short  pen- 
dulum can  be  easily  found  JTIG  2n 
for  most  musical  intervals. 

Figure  211  shows  some  of  the  simpler  figures  that  can  be  ob- 
tained if  the  ratios  of  vibrations  are  such  as  1:2,   2:3,    3:4. 


VIBRATION 


231 


If    the  ratios   are  of  large  numbers,   the  figures  become  more 
complicated. 

237.  Manometric  Flames.  —  The  optical  method  devised 
by  Dr.  Konig,  to  which  he  gave  the  name  of  manometric 
flames,  consists  of  bringing 
the  condensations  and  rare- 
factions of  sound  waves  to 
act  upon  a  gas  flame  and 
regulate  its  height,  and  of 
observing  the  effect  in  a  re- 
volving mirror.  The  prin- 
ciple of  the  apparatus  is  shown  in  Fig.  212,  and  the  com- 
plete form  in  Fig.  213.  A  wooden  or  metal  box  is  divided 
into  two  chambers,  A  and  B,  by  an  elastic  diaphragm  D. 

Two  pipes  open  into  A 
and  one  into  B.  The 
pipe  C  brings  in  gas, 
which  is  burned  as  a 
small,  round  flame  at 
the  top  of  the  tube  E. 
The  pipe  H  opens  into 
B  and  conveys  the 
sound  waves  made  be- 
fore its  open  end  at 
M .  When  D  is  struck 
by  a  condensation,  it 
bends  toward  A,  mak- 
ing that  chamber 
smaller,  increasing  the 
pressure,  and  making 
the  flame  burn  higher  at  E.  When  a  rarefaction  comes  to  D, 
the  chamber  A  is  made  larger,  the  pressure  is  decreased,  and 


232 


SOUND 


the  flame  drops  down  to  a  shorter  one.  These  changes 
follow  one  another  so  rapidly  that  the  eye  cannot  detect 
them  unless  the  image  of  each  flame  is  separated  from  the 
others.  This  can  be  done  in  two  ways :  first,  by  turning  the 
eye  quickly  and  throwing  the  line  of  sight  across  the  flame, 
when  the  images  will  be  separated  in  the  eye ;  and  second,  by 
the  use  of  a  revolving  mirror.  If  the  mirror  is  turned  while 
the  flame  is  burning  steadily,  the  reflection  of  the  flame  seen 
in  the  mirror  will  be  a  plain  band  of  light;  but  if  a  simple 

tone  is  sung  into  the 
mouth  M ,  the  rise  and 
fall  of  the  flame  will  show 
itself  as  a  succession  of 
pointed  reflections  of 
equal  height,  leaning  in 
the  direction  opposite  to 
the  rotation  of  the  mir- 
ror, as  in  Fig.  214,  A. 
If  now  the  octave  of  this 
tone  is  sung,  the  reflec- 
tion will  have  twice  the  number  of  points.  If  the  tone  sung 
is  accompanied  by  overtones,  the  reflection  will  show  a  com- 
pound form  in  which  smaller  waves  are  impressed  upon  the 
fundamental  as  in  Fig.  214,  B. 

NOTE.  —  Experiments  with  vibrating  flames  and  rotating  mirror 
will  not  give  satisfaction  unless  carried  on  in  a  dark  room. 

Demonstration.  —  Sing  the  tones  of  the  scale  before  the  mouth- 
piece, calling  each  tone  0.  Notice  the  change  for  each  pitch.  Re- 
peat with  do,  re,  mi,  etc.  Can  you  tell  a  simple  tone  from  a  com- 
pound one? 

238.  Helmholtz  Resonators  are  spherical  shells,  of  various 
sizes,  each  having  at  one  side  a  short  tube  to  receive  the 


FIG.  214 


VIBRATION 


.233 


FIG.  215 


sound  and  directly  opposite  a  smaller  tube  which  is  held 
to  the  ear.  Each  resonator  will  increase  the  loudness  of  a 
tone  of  some  particular  pitch  only,  whether  that  tone  is 
a  fundamental  or  an  overtone.  These  instru- 
ments were  devised  by  Helmholtz,  and  by 
their  use  he  discovered  just  which  overtones 
are  present  in  the  sounds  of  various  musical  in- 
struments. 

A  modified  form  of  Helmholtz  resonator  is 
shown  in  Fig.  215.  This  consists  of  two  tubes, 
one  of  which  slides  within  the  other  so  -that 
the  instrument  can  be  adjusted  to  tones  of 
varying  pitches.  The  flexible  tube  is  con- 
nected to  the  manometric  flame  apparatus,  and  by  this 
means  the  character  of  the  vibrations  present  is  determined. 
By  combining  sounds  giving  all  the  different  vibrations  ob- 
served, it  is  possible  to  reproduce  a  sound  having  the  same 
quality  as  the  original. 

239.  Musical  Flames.  —  The  air  in  a  tube  may  be  thrown 
into  sound  vibrations  by  means  of  a 
small  flame. 

Demonstration.  —  Procure  a  glass  tube 
about  8  mm.  in  diameter  and  about  20  cm. 
long  and  draw  it  down  to  a  small  jet. 
Bend  this  tube  at  right  angles  and  fasten 
it  to  a  small  board  with  a  wire  staple. 
Place  this  under  a  tripod  covered  with  wire 
gauze,  as  shown  in  Fig.  216.  Turn  on  the 
gas  and  light  it  above  the  gauze.  Regulate 

the  position  of  the  glass  tube  and  the  pressure  of  the  gas  until  you 
have  a  nickering  blue  flame,  broad  at  the  base  and  pointed  at  the 
top.  Place  over  this  a  tube  5  cm.  in  diameter  and  of  almost  any 


FIG.  216 


234 


SOUND 


length,  and  it  will  at  once  give  out  a  loud  musical  tone.     Compare 
the  pitches  given  by  tubes  of  different  lengths. 

240.  Sensitive  Flames.  —  Demonstration.  —  Select  a  piece  of 
small  glass  tubing  and  draw  it  to  a  point  in  the  Bunsen  flame, 
leaving  a  fine  opening.  Connect  the  other  end,  by 
means  of  a  rubber  tube,  to  a  gas  supply,  and  if  you 
have  the  right  size  of  hole  in  the  tube,  and  the  right 
pressure  of  gas,  which  is  generally  greater  than  city 
gas  mains  supply,  you  will  get  a  long  line  of  flame, 
as  in  A  (Fig.  217),  that  is  just  on  the  point  of  flaring. 
Make  any  kind  of  a  sharp  sound,  and  the  flame  will 
at  once  drop  down  to  the  form  of  B,  and  will  keep 
flaring  in  that  form  as  long  as  the  sound  continues. 
A  shrill  whistle,  the  rattle  of  keys,  or  any  hissing 
sound  will  produce  the  same  effect,  showing  that 
this  is  a  very  sensitive  form  of  flame.  Does  the 
rapid  change  in  pressure  at  the  mouth  of  the  tube, 
caused  by  the  waves  of  condensation  and  rarefaction 
due  to  the  high  pitch  of  these  sounds,  explain  the 
action  of  the  flame?  Test  this  flame  by  giving  a 
shrill  whistle  outside  of  the  room  when  the  door  is 
closed. 


FIG.  217 


241.  The  Phonograph,  invented  by  Edison,  consists  of  a 
cylinder  of  specially  prepared  wax  upon  which  the  vibrations 
of  a  diaphragm  are  recorded  by  means  of  a  fine  metal  point 
or  chisel  attached  to  the  diaphragm.  The  waves  of  sound 
throw  the  diaphragm  into  vibration,  this  sets  the  point  in 
motion,  and  as  the  wax  cylinder  is  rotated  the  point  cuts  a 
series  of  spiral  grooves.  These  grooves  are  made  up  of  mi- 
nute indentations  which  correspond  to  the  condensations 
and  rarefactions  of  the  sound  waves.  By  means  of  a  special 
form  of  point  which  takes  the  place  of  the  cutting  tool,  and 
follows  in  the  groove  which  it  has  cut,  the  sound  can  be  re- 
produced with  remarkable  fidelity. 


VIBRATION  235 

Other  instruments  for  the  reproduction  of  sound  make 
use  of  a  disk  for  the  reproducing  surface. 

242.  Limit  of  Audibility.  —  Every  one  knows  that  the 
range  of  voice  differs  for  different  people,  one  person  singing 
tenor,  another  alto,  and  so  on.  There  is  a  somewhat  similar 
range  in  hearing,  some  ears  being  more  sensitive  to  the  high 
pitches,  and  some  to  the  low. 

Demonstration.  —  Procure  a  Galton's  whistle,  which  consists  of 
a  small  brass  whistle  with  a  rubber  bulb  at  one  end  and  a  screw  for 
adjusting  the  pitch  at 
the  other.  Press  the 
bulb  when  the  screw  is 
nearly  out,  and  a  rather 

low    whistle     will    be 

,         m          .      i*.  FIG.  218.  —  Galton's  Whistle 

heard.       Turn   in  the 

screw  a  little,  and  sound  again.  The  pitch  is  higher.  In  this  way 
make  the  pitch  steadily  higher  and  higher,  and  it  will  be  found  that 
first  one  member  of  the  class  and  then  another  will  be  unable  to  hear 
the  whistle. 

Questions 

1.  Does  it  change  the  pitch  of  a  sonometer  string  to  draw  the 
bow  more  vigorously? 

2.  Which  string  on  a  violin  is  the  smallest  ?     Why  ? 

3.  Why  is  the  G  string  on  a  violin  wound  with 
wire? 

4.  What  is  the  explanation  of  the  cracking  of 
a  test  tube  by  holding  it  at  the  top  and  drawing 
a  damp  towel  from  top  to  bottom  ? 

6.  Suppose  Fig.  219  to  represent  the  open  end 

of  a  bell  jar  which  is  struck  a  light  blow  at  A 
FIG  219 

driving  the  rim  toward  the  center.     What  will 

take  place  at  the  points  B,  C,  and  D,  and  where  will  the  nodes  be 
located? 


236  SOUND 

6.  Suppose  you  wish  to  produce  a  low  tone  on  an  organ  pipe  and 
you  want  the  pipe  to  be  as  short  as  possible.     Would  you  use  an 
open,  or  closed  pipe? 

7.  In  what  respects  does  the  sound  produced  by  a  wooden  organ 
pipe  1  m.  long  differ  from  that  given  by  a  metal  pipe  of  the  same 
length?     In  what  respects  is  it  the  same? 

8.  Where  does  the  sand  collect  on  a  vibrating  plate?      Why? 

9.  How  would  you  establish  the  formation  of  a  node  in  a  vibrat- 
ing plate? 

Problems 

1.  If  a  sonometer  string  1  m.  long  gives  128  vibrations  per 
second,  what  must  be  the  length  of  a  similar  string,  stretched  with  the 
same  weight,  to  give  192  vibrations?    What  tone  will  it  give? 

2.  At  what  distance  from  the  bridge  of  a  violin  must  the  finger 
be  placed  to  produce  the  octave  of  the  open  string? 

3.  A  string  1  m.  long  and  2  mm.  in  diameter  makes  150  vibra- 
tions per  second.     Find  the  number  of  vibrations  it  will  give  if  the 
length  is  doubled;  if  the  tension  is  made  4  times  as  great. 

4.  What  will  be  the  length  in  cm.  of  the  part  of  a  string  1  m. 
long  that  will  give  each  tone  of  the  major  scale? 

6.  What  is  the  wave  length  of  the  tone  of  a  closed  organ  pipe 
3  ft.  long?    How  long  must  an  open  pipe  be  to  give  the  same  tone? 

6.  How  long  must  an  open  organ  pipe  be  to  give  the  octave  of 
middle  C  at  0°  C.? 

7.  How  many  vibrations  will  the  pipe  in  problem  6  give  if  the 
end  is  closed? 

8.  What  must  be  the  length  of  the  short  pendulum  of  Fig.  210 
to  make  the  ratio  of  vibrations  3 : 2  if  the  length  of  the  pendulum 
as  a  whole  is  1  m.?    What  must  be  its  length  to  give  the  ratio 
CiE? 

9.  What  is  the  length  of  the  air  column  in  the  Galton  whistle, 
Fig.  218,  when  it  gives  16,000  vibrations  per  second,  the  temperature 
being  20°  C.?    What  is  the  wave  length  of  the  sound  produced? 

10.  A  steamboat  whistle  has  a  wave  length  of  34  ft.     What  tone 
does  it  give? 


CHAPTER  VII 
HEAT 

I.    TEMPERATURE  AND  ITS  MEASUREMENT 

243.  Heat  a  Form  of  Energy.  —  According  to  the  modern 
kinetic  theory  of  heat,  the  molecules  of  all  bodies  are  in  a 
state  of  rapid  vibration,  and  any  increase  of  the  rapidity 
of  this  motion,  from  whatever  cause,  increases  the  heat  of 
the  body,  while  the  heat  is  decreased  if  this  velocity  is  di- 
minished. 

Heat  is  a  form  of  molecular  energy  which  may  be  pro- 
duced by  other  forms  of  energy,  and  is  itself  convertible  into 
other  forms. 

244.  Temperature.  —  The  terms  "  hot  "  and  "  cold  "  are 
purely  relative.     Whether  one  body  is  hotter  or  colder  than 
another  depends  upon  whether  it  can  itself  impart  heat  to  the 
second  body,  or  receive  heat  from  it.    The  condition  of  a  body 
in  this  respect  is  called  its  temperature,  and  depends  directly 
upon  its  molecular  kinetic  energy.     If  m  is  the  mass  of  one 
of  the  molecules  of  a  body,  and  v  its  average  velocity  at  a 
certain  temperature,  the  expression  for  its  molecular  kinetic 
energy  (Formula  20)  is  J  mi)2.     Hence  the  temperature  of 
a  body  is  directly  proportional  to  the  square  of  the  average 
velocity  of  its  molecules. 

If  one  body  is  put  into  contact  with  another,  the  one  that 
has  the  higher  temperature  will  lose  some  of  its  heat,  and  the 

237 


238 


HEAT 


FIG.  220 


one  that  has  the  lower  temperature  will  gain  heat,  until  they 
both  finally  come  to  the  same  temperature. 

Temperature  must  not  be  mistaken  for  quantity  of  heat. 
A  cup  of  hot  water  taken  from  a  pailful  will  have  the  same 
temperature,  but  will  contain  very  little  heat  in  comparison 
with  the  water  in  the  pail. 

245.  The  Physical  Effect  of  Heat  upon  Bodies.  —  There 
are  two  main  results  that  may  come  from  applying  heat  to 

a  body.  One  is  a  change 
in  its  volume,  and  the 
other  is  a  change  in  its 
physical  condition. 

Demonstrations.  —  Make  a 
piece  of  apparatus  like  that 
shown  in  Fig.  220,  as  follows:  Set  two  upright  posts  in  a  base- 
board. Bore  in  each  post,  near  the  top,  a  hole  large  enough  to 
take  a  brass  wire  i  in.  in  diameter.  Fasten  one  end  of  the  wire  to 
one  post  by  a  screw  in  the  top  and  let  the  wire 
pass  loosely  through  the  other  post.  Connect 
a  battery  and  electric  bell  with  the  wire,  and  let 
the  other  end  of  the  circuit  be  connected  with  a 
thin  brass  spring  just  beyond  the  movable  end  of 
the  wire.  Adjust  the  spring  carefully  and  bring 
the  flame  of  a  Bunsen  burner  against  the  wire. 
The  heat  will  expand  the  wire,  which  will  make 
contact  with  the  spring,  when  the  electrical 
circuit  will  be  completed  and  the  bell  will  ring. 
Remove  the  flame;  the  wire  will  contract,  the 
contact  will  be  broken,  and  the  bell  will  stop 
ringing. 

Fit  to  the  mouth  of  a  test  tube  a  rubber  stopper 
with  a  single  hole.    Thrust  a  piece  of  glass  tubing, 
about  30  cm.  long,  through  the  stopper.     Fill 
the  test  tube  with  water  and  push  in  the  stopper  until  the  water 
Btands  at  some  point,  as  A  (Fig.  221).    Take  the  tube  by  the  end 


FIG.  221 


TEMPERATURE  AND  ITS  MEASUREMENT       239 

and  lower  the  test  tube  into  a  beaker  of  hot  water.  The  first  effect 
is  that  the  water  in  the  small  tube  will  drop  to  B.  What  is  the 
cause  of  this?  The  second  effect  is  that  the  water  will  then  begin 
to  rise  and  will  finally  run  over  the  top  C.  Why? 

Empty  the  test  tube,  and  let  it  become  dry  and  cool.  Introduce 
a  short  column  of  water  into  the  middle  of  the  small  tube,  hold  it 
in  a  horizontal  position,  and  push  in  the  stopper  as  before.  Clasp 
the  test  tube  in  the  hand  and  watch  the  position  of  the  water 
index. 

There  are  many  practical  uses  of  the  expansion  of  solids 
when  heated.  A  tire  for  a  wooden  wagon  wheel  is  made 
of  a  size  slightly  smaller  than  the  circu  nf erence  of  the 
wheel ;  to  put  it  on,  the  tire  is  heated,  driven  into  place  on 
the  wheel,  and  on  cooling  becomes  small  enough  to  be  held 
very  firmly.  Large  guns  are  built  up  by  forcing  heated 
steel  rings  over  a  steel  core  and  letting  them  shrink  on, 
after  which  the  guns  are  bored  out  and  rifled. 

246.  Measurement  of  Temperature.  —  The  idea  of  the 
temperature  of  a  body  that  we  receive  from  our  sensations 
is  so  dependent  upon  other  things  than  the  temperature, 
that  it  is  frequently  incorrect.  What  seems  a  high  tempera- 
ture to  one  person  may  seem  a  low  temperature  to  another, 
and  the  same  temperature  seems  different  to  us  at  one  time 
from  what  it  does  at  another.  If  one  hand  is  wet  and  the 
other  dry  and  both  are  held  in  the  current  of  warm  air  coming 
from  a  register,  the  air  will  feel  warm  to  the  dry  hand  and  cold 
to  the  wet  hand.  In  this  and  similar  ways  we  find  that  the 
body  is  not  a  good  instrument  with  which  to  measure  tem- 
perature. The  instrument  that  is  used  for  this  purpose  is 
called  a  thermometer.  The  principle  employed  is  that  of 
the  unequal  expansion  of  bodies  when  heated.  The  most 
common  form  is  the  mercury  thermometer,  which  consists 


240 


HEAT 


of  a  glass  tube  with  thick  walls  and  a  small  bore,  blown  into 
a  bulb  at  one  end  for  holding  the  mercury. 

247.  Filling  the  Thermometer.  —  The  air  is  partly  driven 
from  the  bulb  by  heating  it,  the  open  end  of  the  tube  is  put 
into  mercury,  and  some  of  the  mercury  is  driven  into  the 
bulb  by  the  atmospheric  pressure  when  the  bulb  cools.     By 
repeating  the  process  the  bulb  and  tube  are  entirely  filled. 
The  mercury  is  then  heated  to  a  high  temperature,  and  the 
tube  is  sealed  at  the  top  and  left  air-tight. 

248.  The  Fixed  Points.  —  Since  the  boiling  point  and  the 
freezing  point  of  pure  water  are  always  the  same  under  the 

same  pressure,  these  points  are  taken  as  the 
fixed  points  for  the  thermometer. 

The  freezing  point  is  determined  by 
placing  the  bulb  and  part  of  the  stem  in 
snow  or  finely  crushed  ice,  contained  in  a 
suitable  vessel  (Fig.  222).  The  point  at 
which  the  end  of  the  mercury  column  comes 
to  rest,  when  close  to  the  ice,  is  marked  as 
the  freezing  point. 

The  boiling  point  is  fixed  by  suspending 
the  thermometer  in  the  steam  from  boiling 
pure  water.     The  bulb  should  be  at  least 
an  inch  above  the  water  and   the  boiler 
should  be  tall  enough  so  that  the  mercury 
will  come  only  just  above  the  stopper  by 
which  it  is  supported.     Whenever  the  steam 
is  coming  briskly  from  the  escape  pipe  and  the  mercury  has 
ceased  to  rise,  the  end  of  the  column  is  marked  as  the  boiling 
point,  provided  the  barometer  reads  760  mm.  at  the  time. 


TEMPERATURE  AND  ITS  MEASUREMENT       241 

The  manometer  tube  m  (Fig.  223)  shows  whether  the  pressure  of 
the  steam  is  the  same  as  that  of  the  atmosphere.  If  this  is  not  the 
case,  a  correction  has  to  be  made  since  the 
temperature  of  steam  rises  rapidly  with 
an  increase  of  pressure.  When  the  pres- 
sure is  near  760  mm.,  an  increase  of  27 
mm.  in  the  pressure  produces  a  change  of 
1°  C.  in  the  boiling  point. 

249.  Graduating  the  Scale.— The 

bore  of  the  thermometer  tube  should 
be  of  uniform  diameter  throughout 
its  length.  At  ordinary  tempera- 
tures, equal  increases  of  temperature 
will  then  cause  practically  equal 
amounts  of  elongation  of  the  mercury 
column  in  any  part  of  the  tube; 
hence,  when  the  kind  of  scale  has  been 
decided  upon,  the  length  between 
the  freezing  and  boiling  points  is  di- 
vided into  equal  parts,  called  degrees. 


FIG.  223 

250.  Thermometric  Scales.  —  The  scales  in  most  general 
use  in  this  country  are  the  Centigrade,  or  hundred-degree 
scale  of  Celsius,  which  makes  the  freezing  point  of  water 
zero  (0°)  and  its  boiling  point  100°;  and  the  Fahrenheit, 
which  makes  the  freezing  point  32°,  the  boiling  point  212°, 
and  puts  the  zero  32°  below  the  freezing  point.  In  both 
scales,  readings  that  are  below  zero  are  designated  by  the 
minus  sign,  as  —  10°  C.  The  Fahrenheit  scale  is  the  one  in 
common  use  in  the  United  States,  but  the  Centigrade  has  been 
adopted  for  scientific  work  on  account  of  its  greater  conven- 
ience. Unless  otherwise  mentioned,  the  Centigrade  scale 
will  be  used  in  this  work. 


Rev. 


242 


HEAT 


251.  Comparison  of  Centigrade  and  Fahrenheit  Readings. 

—  Since  the  Centigrade  scale  has  100  degrees  between  the 
fixed  points,  and  the  Fahrenheit  180,  it  is  evi- 
dent that  100  C.  degrees  =  180  F.  degrees,  and 
°  hence  1  C.  degree  =  f  F.  degree,  and  1  F. 
degree  =  f  C.  degree.  When  the  reading  of 
one  scale  is  to  be  transformed  into  the  equiva- 
lent reading  on  the  other,  the  differing  posi- 
tions of  the  zero  point  must  be  considered. 
These  formulas  may  be  used : 


o 


-40 


or 


C  =  f  (F  -  32°) 
F  =  |  C  +  32° 

C    =F--32 

100         180 


(45) 
(46) 

(47) 


-40" 


FIG.  224 


Another  formula  is  based  upon  the  fact  that  —40° 
indicates  the  same  temperature  on  both  scales. 
Hence  to  change  a  F.  reading  to  a  C.  reading,  add 
40°  to  the  F.  reading,  multiply  the  sum  by  f ,  and 
subtract  40°  from  the  product : 

C  =  f  (F  +  40)  -  40  F  =  |  (C  +  40)  -  40 


252.  Limitations  of  Mercury  Thermometers. — The  glass 
bulb  of  a  thermometer  may  gradually  change  in  volume. 
There  may  also  be  a  temporary  change  after  use  for  high  tem- 
peratures in  which  the  bulb  returns  slowly  to  its  original 
volume.  A  thermometer,  therefore,  should  be  frequently 
tested  to  determine  what  correction  is  necessary,  in  reading. 

For  very  low  temperatures  alcohol  is  used  instead  of  mercury, 
which  freezes  at  —  39°  C.  The  ordinary  form  of  mercury 
thermometer  cannot  be  used  for.  temperatures  above  350°  C., 
since  its  boiling  point  is  357°  C.  When  the  space  above  the 
mercury  column,  however,  is  filled  with  nitrogen  under  pres- 


TEMPERATURE  AND  ITS  MEASUREMENT       243 


sure,  it  can  be  used  for  temperatures  up  to  550°  C.  For  still 
higher  temperatures  the  air  thermometer  or  the  electric 
pyrometer  is  used. 

253.  The  Air  Thermometer.  —  A  simple  air  thermometer 
(Fig.  225)  can  be  made  by  thrusting  the  tube  of  an  air  ther- 
mometer bulb  through  a  rubber  stopper  with  two 
holes,  and  fitting  this  stopper  to  a.  test  tube  or 
bottle  nearly  full  of  colored  water.  A  scale  along 
the  side  is  used  for  reading  the  height  of  the  water 
column,  which  is  introduced  by  driving  out  a  few 
bubbles  of  air  from  the  bulb  by  heating  it.  When 
the  air  cools,  the  water  will  rise  in  the  stem  (Fig.  225). 
The  position  of  the  water  column  is  affected  by  the 
varying  pressure  of  the  air  as  well  as  by  the  tem- 
perature, so  that  it 
will  not  correspond 
directly  with  the  read- 
ings cf  the  mercurial 
thermometer.  FIG.  225 

254.  Metallic  Thermome- 
ters.— A  compound  bar  made 
by  riveting  together  two  thin 
strips  of  brass  and  iron  will, 
when  heated,  form  an  arc  of 
a  circle,  with  the  brass  on  the 
outside.  This  unequal  ex- 
pansion of  two  metals  is  the 
regulating  principle  in  the 
metallic  thermometer.  A  convenient  form  is  made  by  fasten- 
ing the  two  metals  together  in  the  form  of  a  spiral  spring, 
having  on  the  outside  the  one  with  the  greater  rate  of  ex- 


FIG.  226 


244 


HEAT 


pansion.  One  end  of  the  spring  is  fixed,  and  the  other  end 
acts  upon  a  pointer  which  marks  off  the  temperature  on 
a  scale  on  the  face  of  the  instrument.  Figure  226  shows  a 
self-recording  thermometer  of  this  type.  The  time  card  is 
rotated  once  per  day  by  clockwork,  while  the  record  is  made 
by  a  pen  at  the  end  of  the  pointer. 

255.  The  Clinical  Thermometer  is  used  in  taking  the 
temperature  of  the  human  body.  The  tube  of  this  ther- 
mometer is  pinched  nearly  together  near  the  lower  end. 
When  the  thermometer  cools,  the  mercury  column  breaks 
at  this  narrowest  part,  and  the  column  in  the  tube  remains 


FIG.  227.  —  Clinical  Thermometer 

just  as  it  was  at  the  highest  temperature  during  the  time 
of  its  use ;  the  reading,  therefore,  can  be  taken  at  any  time. 
Before  it  is  used  again,  the  column  is  reduced  by  a  jerking 
motion  which  forces  some  of  the  mercury  past  the  constric- 
tion into  the  bulb. 

256.  Maximum  and  Minimum  Thermometers  are  used  by 
the  stations  of  the  Weather  Bureau  to  show  the  highest 
and  lowest  temperatures  during  each  day.  One  form  of 


FIG.  228.  —  Minimum  and  Maximum  Thermometers 

maximum  instrument  is  made  like  the  clinical  thermometer. 
After  being  read  it  is  set  by  swinging  it  around  in  a  circle, 


TEMPERATURE  AND  ITS  MEASUREMENT       245 

so  that  the  centrifugal  force  drives  the  mercury  back  into 
the  bulb,  and  the  instrument  is  then  ready  for  the  next  day. 
One  form  of  minimum  thermometer  is  an  alcohol  thermometer 
with  a  small  glass  spool  or  index  moving  loosely  in  the  tube. 
This  is  drawn  down  by  surface  tension  whenever  the  end  of 
the  liquid  column  touches  the  end  of  the  spool  as  the  liquid 
contracts;  but  when  it  expands,  the  liquid  runs  past  the 
spool  and  leaves  it  at  the  point  of  lowest  temperature.  To 
set  this  thermometer  it  is  merely  necessary  to  tip  the  tube 
slightly,  and  the  spool  will  run  to  the  end  of  the  liquid  column 
and  stop. 

Questions 

1.  Suppose  a  basin  (^4)  to  be  partly  filled  with  ice  water,  another 
(B)  with  tepid  water,  and  a  third  (C)  with  warm  water.     If  the 
left  hand  is  thrust  into  A,  the  right  hand  into  C,  and  after  a  time 
both  are  thrust  into  B,  how  will  the  water  in  B  feel  to  the  left  hand 
and  how  to  the  right  hand  ?     What  does  this  teach  ? 

2.  What  is  the  difference  between  quantity  of  heat  and  tempera- 
ture? 

3.  Why  is  one  end  of  a  railroad  bridge  sometimes  placed  upon 
small  rollers? 

4.  Which  expands  more   with  a  rise  of  temperature,  the  glass 
bulb  of  a  thermometer  or  the  mercury  that  it  contains?    What 
proof  have  you? 

6.  Why  is  a  wagon  tire  put  on  when  hot  ? 

6.  What  would  be  the  effect  of  placing  a  football  on  a  warm 
radiator? 

7.  What  is  the  reading  of  the  fixed  points  of  a  thermometer? 
Why  are  they  called  fixed  points? 

8.  What  is  assumed  when  the  length  of  a  thermometer  stem 
between  0°  and  100°  is  divided  into  100  equal  parts? 

9.  Suppose  that  a  compound  bar  is  made  of  two  metals,  A  on 
the  right  and  B  on  the  left.     If  A  expands  more  than  B,  which  will 
be  on  the  outside  of  the  curved  bar  when  the  temperature  rises  ? 


246  HEAT 

10.  Why  does  the  mercury  column  in  a   clinical  thermometer 
break  when  it  cools  after  being  used  ? 

11.  Suppose  you  wish  to  take  a  temperature  quickly.     Would  you 
use  a  thermometer  with  a  large  or  a  small  bulb?     Why? 

12.  Suppose  you  need  to  observe  very  slight  changes  of  tempera- 
ture.    Would  you  use  a  thermometer  with  a  large  or  a  small  bore? 
Why? 

Problems 

1.  What  change  in  Fahrenheit  degrees  corresponds  to  a  change 
of  25  Centigrade  degrees  ? 

2.  If  the  change  in  Fahrenheit  degrees  is  27,  what  is  the  equiva- 
lent change  in  Centigrade  degrees? 

3.  What  Fahrenheit  reading  corresponds  to  the  reading  25°  C.  ? 

4.  What  Centigrade  reading  corresponds  to  the  reading  27°  F.  ? 

5.  For  what  temperature  do  the  Centigrade  and  Fahrenheit 
thermometers  give  the  same  reading? 

6.  The  normal  temperature  of  the  body  is  98.4°  F.     What  is  it 
in  the  Centigrade  scale  ? 

7.  Seventy-six  degrees  is  called  Summer  Temperature  on  a 
Fahrenheit  thermometer.     What  will  be  its  reading  on  a  Centi- 
grade thermometer? 

8.  The  boiling  point  of  liquid  air  is  -  192.2°  C.     What  is  this 
temperature  on  the  Fahrenheit  scale  ? 

9.  The  melting  point  of  iron  is  1520°  C.     What  Fahrenheit 
reading  indicates  the  same  temperature  ? 

10.  The  temperature  of  a  room  changed  17  Fahrenheit  degrees. 
What  was  the  change  in  Centigrade  degrees  ? 

11.  PRODUCTION  AND  TRANSMISSION  OF  HEAT 

257.  Sources  of  Heat.  —  The  principal  sources  of  heat 
are  the  sun;  the  interior  of  the  earth;  mechanical  sources 
such  as  friction,  impact,  and  compression,  in  which  work  is 
changed  into  heat ;  chemical  action,  in  which  chemical  energy 
is  transformed  into  heat ;  and  the  heat  caused  by  the  passage 
of  an  electric  current. 


PRODUCTION  AND  TRANSMISSION  247 

That  the  sun  is  a  source  of  heat  needs  no  proof,  while  the 
experience  of  miners  working  in  deep  mines  proves  that  there 
is  internal  heat,  the  temperature  rising  as  the  distance  from 
the  surface  increases. 

258.  Friction.  —  There   are   many   familiar   examples   of 
the, heating  effects  of  friction.     The  train  of  sparks  that 
fly  from  a  sleigh  runner  as  it  passes  over  a  stone,  and  the 
sparks  that  come  from  a  car  wheel  when  the  brake  is  applied, 
both  show  that  great  heat  is  generated  by  the  friction ;  for 
the  sparks  are  burning  iron.     The   hands  are  warmed  by 
rubbing.     A  match  is  set  on  fire  by  friction,  and  a  piece  of 
wood  in  a  turning  lathe  is  charred  when  the  corner  of  another 
piece  is  held  against  it. 

259.  Impact.  —  When  two  bodies  meet  in  collision,  the 
effect  of  the  blow  is  to  increase  the  rate  of  vibration  of  the 
molecules,  and  hence  to  raise  the  temperature  of  the  bodies. 
An  example  of  this  is  seen  in  the  fact  that  one  end  of  an  iron 
bar  can  be  heated  by  placing  it  on  an  anvil  and  striking  it 
several  vigorous  blows. 

260.  Compression.  — When  a  gas  is  suddenly  compressed 
there  is  a  corresponding  sudden  rise  in  its  temperature. 
In  steam  air  compressors  of  the  double  cylinder  type,  the 
heated  air  coming  from  the  first  compressor  cylinder  is  cooled 
before  going  into  the  second  by  being  passed  through  pipes 
surrounded  by  cold  water. 

261.  Chemical    Action.  —  Many    chemical    combinations 
give  rise  to  heat.     The  most  familiar  of  these  is  the  com- 
bination of  oxygen  with  carbon,  as  seen  in  combustion ;  for 
example,  the  burning  of  a  match  or  of  coal.     If  1  c.c.  of  con- 
centrated sulphuric  acid  is  poured  into  4  c.c.  of  water  in  a  test 


248  .  HEAT 

tube,  both  liquids  being  at  the  room  temperature,  it  will 
be  found  that  the  mixture  is  several  degrees  hotter.  Animal 
heat  is  due  to  oxidation  within  the  body. 

262.  The  Transmission  of  Heat.  —  When  two  bodies  are 
brought  in  contact  with  each  other,  each  communicates  a 
part  of  its  molecular  energy,  or  heat,  to  the  other.     If  the 
two  bodies  are  of  the  same  temperature,  each  receives  as 
much  as  it  imparts,  and  there  is  no  change  in  the  temperature 
of  either.     If,  however,  the  body  A  is  of  a  higher  temperature 
than  the  body  B,  it  gives  more  heat  than  it  receives,  and  its 
temperature  is  lowered  by  an  amount  which  depends  upon 
the   difference   between   the   two   temperatures;  while  the 
body  B  has  its  temperature  raised,  and  we  say  heat  has  been 
transmitted  to  it.     Heat  can  be  transmitted  in  three  ways  — 
by  conduction,  by  convection,  and  by  radiation. 

263.  Conduction ;  Conductivity  of  Solids.  —  If  one  end  of  a 
copper  wire  10  cm.  long  is  held  in  the  hand  and  the  other 
end  is  placed  in  the  flame  of  a  Bunsen  burner,  the  end  in  the 
flame  will  become  red-hot,  and  in  a  short  time  the  end  in  the 
hand  will  become  uncomfortably  warm.     This  method,  of 
transmission,  by  which  the  heat  is  transferred  from  molecule 
to  molecule  along  the  body,  is  called  conduction.     If  the  same 
experiment  is  made  with  a  glass  tube,  the  glass  can  be  melted 
to  within  4  or  5  cm.  of  the  fingers  without  burning  them, 
while  a  stick  can  be  burned  to  the  very  fingers  without  harm. 

These  three  examples  illustrate  bodies  that  are  good, 
medium,  and  poor  conductors  of  heat.  A  good  conductor 
feels  either  warmer  or  colder  than  a  poor  conductor  if  not 
at  the  same  temperature  as  that  of  the  hand.  This  is  due 
to  the  fact  that  it  conveys  its  heat  to  the  hand,  or  takes 
heat  from  the  hand,  more  readily  than  the  poor  conductor, 


PRODUCTION  AND   TRANSMISSION 


249 


Silver 


TABLE   OF   RELATIVE   CONDUCTIVITIES 
1000     Lead 


85 


Copper 736    Platinum 63 


Brass 
Tin 


235     German  silver     ......     60 

145     Glass  20 


Iron 119     Wood  lengthwise  of  the  grain    .       3 

264.  The  Davy  Safety  Lamp.  —  It  frequently  happens 
that  an  explosive  mixture  of  gases  accumulates  in  some 
part  of  a  mine.  An  ordinary  lamp  brought  in 
contact  with  this  mixture  would  cause  an  ex- 
plosion. To  prevent  this,  and  still  make  it 
possible  to  use  a  light,  Sir  Humphry  Davy  de- 
vised a  form  of  lamp  in  which,  as  the  illustra- 
tion shows,'  the  flame  is  entirely  surrounded 
with  wire  gauze.  Whenever  the  lamp  is  brought 
into  an  inflammable  mixture  of  gases,  some  of 
the  mixed  gas  will  enter  the  lamp  and  burn 
there.  But  so  great  is  the  heat  conductivity 
of  the  gauze  that  the  gas  outside  the  lamp  does 
not  receive  heat  enough  to  take  fire  until  the 
gauze  becomes  red  hot.  FIG.  229.— 

Davy  Lamp 

An  experiment  that  shows  this  conductivity  can 
be  made  by  placing  a  piece  of  wire  gauze  upon  a  tripod  with  a 

Bunsen  burner  beneath  it. 
The  gas  may  be  lighted  either 
above  or  below  the  gauze, 
and  the  flame  will  not  pass 
through  (Fig.  230). 


265.  Conductivity    of 
Liquids.  —  Liquids    as    a 
FIG.  230  class  are  poor  conductors. 


250 


HEAT 


of    heat,    the   conductivity   of   water  being  about 
that  of  copper. 


of 


Demonstration.  —  Put  some  pieces  of  ice  in  the  bottom  of  a  test 
tube.  Fasten  them  there  with  a  coil  of  wire.  Pour  in  water  until 
the  tube  is  nearly  full,  and  then  hold  it  over 
a  Bunsen  burner  so  that  the  heat  will  be  ap- 
plied at  a  point  covered  by  the  water.  In 
this  way  the  water  in  the  upper  part  of  the 
tube  may  be  boiled  while  there  is  ice  in  the 
bottom  only  a  few  centimeters  away. 


FIG.  231 


Conductivity  of  Gases.  —  Gases 
are  extremely  poor  conductors  of  heat, 
the  conductivity  of  air  being  only  ^Vo  of  that  of  copper! 
Double  windows  prevent  air  currents  that  would  carry 
away  the  heat,  and  on  account  of  the  low  conductivity  of 
air  are  a  protection  from  the  cold. 

The  fur  of  animals  is  an  effi- 
cient protection  because  of  the 
layer  of  air  that  is  connected 
with  it.  The  protection  in  both 
these  cases  consists  in  preventing 
the  heat  from  within  from  escap- 
ing. Practical  use  of  air  spaces 
to  prevent  the  transfer  of  heat  is 
made  in  the  double  walls  of  ice 
houses  and  refrigerators,  for  keep- 
ing the  heat  out,  and  in  fireless 
cookers  for  keeping  the  heat  in. 

Still  better  results  are  obtained 

by  exhausting  the  air  from  between  the  double  walls,  as  in 
the  thermos  bottle,  in  which  either  hot  or  cold  liquids  can 
be  kept  without  much  change  of  temperature  for  some  hours. 


FIG.  232.— Thermos  Bottle 


PRODUCTION  AND  TRANSMISSION 


251 


267.  Convection.  —  If  a  part  of  a  fluid  body  (liquid  or 
gas)  is  heated,  it  expands  (§  245)  and  becomes  lighter,  bulk 
for  bulk,  than  the  other  parts.  As  the  molecules  are  free 
to  move,  the  cooler,  heavier  parts  tend  to  sink  to  the  bottom, 
and  thus  to  push  the  warmer  parts  to  the  top.  There  is  thus 
set  up  an  ascending  current  wherever  any 
part  of  the  liquid  or  gas  at  the  bottom  is 
heated  above  the  rest ;  and  downward  and 
lateral  currents  in  the  cooler  parts.  All 
these  currents  are  called  convection  currents. 


Demonstration.  —  Fit  a  rubber  stopper  with 
two  holes  to  the  mouth  cf  a  thin  glass  flask. 
Through  these  holes  thrust  two  glass  tubes 
about  8  cm.  long,  making  an  end  of  one  nearly 
even  with  the  top  of  the  stopper,  and  an  end  of 
the  other  nearly  even  with  the  bottom.  Fill 
the  flask  with  colored  water  and  heat  it.  Put 
in  the  stopper  and  sink  the  flask  in  a  large  glass 
of  cold  water,  as  in  Fig.  233.  Convection  cur- 
rents will  be  set  up  by  the  warm  water  coming  out  of  one  tube 
while  the  cold  water  goes  into  the  other.  Into  which  will  the 
cold  water  go?  Why? 


FIG.  233 


268.  Heating  Buildings  with  Hot  Water.  —  The  hot  water 
system  has  become  a  very  common  method  of  heating 
buildings.  It  works  by  means  of  the  convection  currents 
that  are  set  up  in  a  system  of  water  pipes  when  a  section 
near  the  bottom  is  heated  more  than  the  rest.  A  miniature 
heating  system  can  be  set  up  and  put  in  operation  by  the  use 
of  the  apparatus  shown  in  Fig.  234.  By  coloring  part  of  the 
water  the  paths  of  the  convection  currents  can  be  readily 
traced.  The  heating  of  a  house  is  only  an  extension  of  this 
experiment. 


252 


HEAT 


FIG.  234 


FIG.  235.  — Hot  Water  Heating  System 


In  the  hot  water  system  shown  in  Fig.  235,  the  hot  water 
leaves  the  heater  by  the  upper  pipes,  goes  through  the  differ- 
ent radiators,  and  then  back  to  the  heater,  which  it  enters  at 

the  bottom.  In  this 
system  the  pipes 
must  be  kept  filled 
with  water.  The 
height  of  water  is 
read  from  a  gauge 
attached  to  the  tank, 
which  is  higher  than 
any  of  the  radiators. 

269.  Convection  in 
Gases. — Air  that  is 
in  contact  with  a 
heated  surface  be- 


F  COLO  Atf) 


FIG.  236.  —  Diagram  of  a  Hot  Air  Furnace 


PRODUCTION  AND  TRANSMISSION  253 

comes  itself  heated,  and  convection  currents  are  .set  up  in 
the  same  way  as  in  liquids.  This  can  be  shown  by  lighting 
a  piece  of  touch-paper  and  holding  it  over  a  piece  of  heated 
metal,  when  the  smoke  will  rise  with  the  current  of  air. 

Convection  currents  in  air  are  made  use  of  in  warm  air 
systems  of  heating.  Cold  air  enters  the  heater  at  the  base, 
and  after  being  heated,  passes  out  through  the  warm  air  de- 
livery tubes,  which  distribute  it  throughout  the  building. 

NOTE.  —  Touch-paper  is  made  by  dipping  filter  paper  or  blotting 
paper  into  a  solution  of  saltpeter.  When  dry  it  \vill  burn  without 
flame,  but  will  give  off  smoke  freely. 

Demonstration.  —  Set  a  short  piece  of  candle  in 
a  saucer  and  light  it.  Set  over  it  a  chimney  from 
a  student  lamp.  Pour  water  into  the  saucer  to 
prevent  air  going  into  the  chimney  from  the 
bottom,  and  the  candle  will  soon  go  out.  Why  ? 
Cut  a  piece  of  tin  of  the  shape  shown  in  (a)  in  Fig. 
237,  and  put  it  down  the  chimney  with  the  wide 
part  resting  on  the  top.  Light  the  candle  again,  _ 
and  it  will  keep  on  burning.  Why?  Examine 
the  air  on  both  sides  of  the  tin,  by  the  smoke  from  touch- 
paper. 

270.  Ventilation.  —  The  preceding  demonstration  shows 
the  need  of  renewing  the  air  in  order  to  support  combustion. 
It  also  shows  that  this  renewal  is  secured  by  means  of  convec- 
tion currents.  A  room  is  ventilated,  more  or  less,  by  con- 
vection currents  through  chimneys,  windows,  and  crevices 
in  floor  and  walls,  whenever  the  temperature  in  the  room 
differs  from  that  outside. 

In  a  house  that  is  heated  by  a  hot-air  furnace,  good  ventila- 
tion is  secured  by  bringing  the  air  to  be  heated  from  outside  th* 
house.  The  distribution  of  the  heated  air  takes  place  in  convection 
currents.  The  difficulty  with  this  method  o#  heating  is  that  it  is 


254 


HEAT 


affected  by  the  direction  of  the  wind,  the  hot  air  going  most  freely 
into  the  rooms  situated  on  the  opposite  side  of  the  house  from  the 

direction  of  the  wind;  into  the 
south  rooms  if  -the  wind  is  from 
the  north,  for  instance.  Figure 
238  shows  how  fresh  air  can  foe  se- 
cured when  hot  water  or  steam 
heating  is  used. 

271.  Radiation  of  Heat. — 
The  third  method  by  which 
heat  may  be  transferred  from 
one  body  to  another  is  by 
radiation.  If  the  open  hand 
is  held  in  front  of  a  stove,  the 
radiant  energy  sent  out  by  the 
fire  is  received  on  the  hand 
and  it  becomes  warm,  though 
the  air  may  not  feel  warm.  If 
a  screen  is  placed  between  the 
FlGt  238  stove  and  the  hand,  the  radia- 

tion is  cut  off.  The  earth  receives  heat  from  the  sun  in  the 
form  of  radiant  energy.  This  radiant  energy  is  defined  as  a 
wave  motion  in  the  ether  which  is  supposed  to  fill  all  space. 
When  the  vibrations  of  the  ether  are  received  by  a  body, 
they  set  its  molecules  into  more  rapid  vibration,  which  raises 
its  temperature,  increasing  its  heat. 

272.  Nature  of  the  Ether. — The  all-pervading  ether  must 
be  elastic  and  rigid,  and  capable  of  displacement  and  of  ex- 
erting pressure.  It  may  be  considered  as  a  universal  jelly, 
so  thin  as  to  pass  readily  through  every  known  substance, 
and  to  permit  the  densest  substance  to  pass  through  it 
as  a  sieve  passes  through  the  air;  a  jelly  so  thin  that  it 


PRODUCTION  AND  TRANSMISSION 


255 


has  no  appreciable  weight  and  has  caused  no  measurable 
change  in  the  velocity  of  any  heavenly  body. 

273.  Laws  of  the  Radiation  of  Heat. 

I.  Radiation  takes  place  through  a  vacuum  as  well  as  in  the 
air.     This  results  from  the  nature  of  the  radiation,  for  the 
medium  by  means  of  which  the  radiation  takes  place  is  the 
ether  and  not  the  air.     If  this  law  were  not  true,  we  should 
receive  no  heat  from  the  sun  and  but  little  from  the  bulb, 
of  an  incandescent  lamp. 

II.  Radiation  in  a  vacuum  or  in  a  homogeneous  substance 
takes  place  in  straight  lines.     A  homogeneous  substance  is 
one  that  has  the  same  physical  structure  throughout. 

III.  The  intensity  of  radiant  heat  is  proportional  to  the 
temperature  of  the  source. 

IV.  The  intensity   is  inversely  proportional 
to  the  square  of  the  distance  from   the  source. 
The  proof  of  this  law  is  like  that  in  §  214,  c. 

274.  The    Radiometer    is    an    instrument 
used  to  detect  radiant  heat.     It  consists  of  a 
glass  bulb  inclosing  two    arms  of  aluminum 
crossing  each  other  at  right  angles  and  carrying 
at  each  end  a  mica  vane,  one  side  of  which 
is  coated  with  lampblack  while  the  other  is 
bright.     These  arms  are  fastened  horizontally 
to  a  vertical  shaft  which  can  rotate  with  them. 
The  air  is  nearly  exhausted  from  the  bulb. 

When  these  vanes  are  subjected  to  the  action  of  radiant 
heat,  they  set  up  a  rotation,  the  velocity  of  which  is  de- 
pendent upon  the  intensity  of  the  heat  received. 


FIG.  239.  — 
Radiometer 


256 


HEAT 


This  is  due  to  the  fact  that  the  molecules  of  rarefied  air  in  their 
vibration  (§  243)  bound  back  and  forth  between  the  vanes  and  the 

walls  of  the  bulb ;  that  the  blackened 
side "  of  each  vane  becomes  warmer 
than  the  other;  and  that  the  mole- 
cules rebound  from  the  warmer  side 
with  greater  speed,  producing  a 
greater  reaction  of  pressure  on  that 
side. 

Demonstration.  —  Make  a  light- 
tight  box,  large  enough  to  hold  a 
radiometer.  Heat  a  flat  piece  of  cast 
iron  or  brass  nearly  to  a  red  heat  and 
fasten  it  to  the  inner  face  of  the  door 
FIQ.  240  of  the  box  (Fig  240).  Put  the  radi- 

ometer into  the  box  and  close  the  door.  Leave  it  closed  for  about 
a  minute  and  on  opening  it  the  radiometer  will  be  found  to  be 
rotating.  Is  it  heat  or  light  that  produces  the  rotation? 

275.  The  Reflection  of  Radiant  Heat.  —  Experiment 
proves  that  radiant  heat  is  reflected  in  accordance  with  the 
following  laws  (compare  with  §  65) : 

I.  The  incident  and  reflected  rays  are  in  a  plane  that  is 
perpendicular  to  the  reflecting  surface. 

II.  The  angle  of  reflection  is  equal  to  the  angle  of  incidence. 
Demonstration.  —  Place  two  concave  mirrors  directly  opposite 

each  other,  as  at  M  and  Mf  (Fig.  241).     In  the  focus  of  M  place  the 

M' 


FIG.  241 


PRODUCTION  AND  TRANSMISSION  257 

radiometer  and  in  the  focus  of  M  '  place  an  iron  ball  heated  nearly 
to  redness.  Have  the  mirrors  far  enough  apart  so  there  will  be 
no  rotation  due  to  direct  radiation  from  the  ball.  When  the  ball 
and  the  radiometer  are  in  the  foci  of  their  respective  mirrors,  the 
radiometer  will  set  up  a  brisk  rotation  due  to  reflected  radiation. 

276.  Radiating  and  Absorbing  Powers.  —  The  radiating 
pow,er  of  a  heated  body  depends  upon  its  temperature  and 
the  character  of  its  surface.     A  body  with  a  smooth,  brightly 
polished  surface  has  a  much  lower  radiating  power  than  one 
of  the  same  material  but  with  a  dull  surface.     Bodies  that 
absorb  heat  readily  are  good  radiators  and  poor  reflectors. 
The  power  of  absorption  depends  somewhat  upon  color. 
This  can  be  shown  by  placing  upon  snow  two  pieces  of  cloth, 
one  black  and  the  other  white.     It  will  be  found  that  when 
the  sun  shines  upon  them,  the  black  piece  will  absorb  heat 
and  melt  its  way  into  the  snow,  while  the  white  will  not. 

277.  Selective  Absorption.  —  The  extent  of  the  absorp- 
tion depends,  in  some  substances,  upon  the  temperature  of 
the  source  of  heat. 

Demonstration.  —  Set  a  radiometer  in  front  of  a  fishtail  gas 
flame  so  near  that  it  will  rotate  briskly.  Place  a  pane  of  glass  be- 
tween them.  Much  of  the  radiation  will  be  absorbed  by  the  glass, 
some  will  be  reflected,  and  the  rotation  will  nearly  stop.  Set  the 
radiometer  in  the  sunshine.  After  it  is  in  motion  hold  the  glass 
plate  between  it  and  the  sun.  Does  the  rotation  stop  ? 

The  fact  that  glass  permits  much  of  the  radiation  from 
the  sun  to  pass  through,  but  does  not  permit  the  passage 
of  radiation  from  bodies  of  much  lower  temperature,  is  of 
great  importance,  since  radiation  from  the  sun  enters  our 
rooms  through  the  windows  and  heats  them,  while  the  radi- 
ant heat  from  stoves  and  radiators  cannot  pass  out. 

The  radiant  heat  that  comes  from  the  sun  and  passes 


258  HEAT 

through  the  glass  readily  is  called  luminous  heat,  because 
it  comes  from  a  source  that  also  gives  light.  Radiant  heat 
that  comes  from  bodies  of  comparatively  low  temperature  and 
is  largely  absorbed  by  the  glass  is  called  nonluminous  heat. 

Substances  like  rock  salt,  which  .permit  radiant  heat  to 
pass  through  them  readily,  are  called  diathermanous ,  while 
those  like  glass  and  water,  that  absorb  radiant  heat,  are 
called  athermanous. 

Demonstration.  —  Place  a  flat  battery  jar  between  a  radiometer 
and  the  sun.  Does  the  rate  of  rotation  change?  Fill  the  jar  with 
water.  Is  there  any  greater  change  ? 

Questions 

1.  How  do  you  explain  the  fact  that  a  meteor  becomes  luminous 
when  it  strikes  our  atmosphere? 

2.  Why  are  the  chips  that  are  turned  from  an  iron  rod  hot? 

3.  Why  is  a  rifle  cartridge  exploded  when  the 
hammer  falls? 

4.  Why  does  a  bicycle  pump  become  warm 
when  used  to  pump  air  into  a  tire?    Give  two 
reasons. 

5.  If  three  wires,  one  of  copper,  one  of  iron, 
and  one  of  German  silver,  are  fastened  on  a  block, 

FIQ.  242          the  projecting  ends  covered  with  paraffin,  and 
thrust  into  a  Bunsen  flame. at  A,  the  paraffin 
will  melt  at  different  rates.    Why?    If  it  melts  6  inches  on  the 
copper  wire,  how  far  will  it  melt  on  each  of  the  other  two? 

6.  Why  is  a  flatiron  handle  made  of  wood  rather  than  of  iron  ? 

7.  To  cool  some  hot  water  by  setting  it  in  a  cold  room,  would 
you  put  it  in  a  tin  pail  or  in  a  wooden  pail?     Why? 

8.  Describe  the  result  of  the  selective  absorption  of  the  glass 
roof  of  a  hothouse  upon  the  temperature  within  it. 

9.  When  an  arc-light  lantern  is  used  to  project  a  microscope 
slide,  why  is  a  water  cell  put  between  the  arc  light  and  the  slide? 

10.  Make  a  diagram  of  walls  suitable  for  an  ice  house. 

11.  Why  does  a  dead  leaf  resting  on  the  snow  sink  into  it  on  a 
sunshiny  day? 


EXPANSION,   FUSION,  AND  VAPORIZATION 


259 


12.  Why  does  a  piece  of  flannel  lying  on  a  marble  table  top  feel 
warm  while  the  marble  itself  feels  cold  ? 

13.  What  is  best  for  a  steam  or  hot  water  radiator,  a  highly 
polished  or  a  dull  surface? 

14.  Why  is  it  that  a  thermos  bottle  will  keep  a  liquid  either  hot 
or  cold? 

III.    EXPANSION,  FUSION,  AND  VAPORIZATION 

278.  The  Measurement  of  Expansion  of  Solids.  —  The 
first  demonstration  in  §  245  proves  that  when  the  temper- 
ature of  a  solid  increases,  the  solid  expands; 
but  that  demonstration  gives  no  definite  idea 
of  the  amount  of  this  expansion.  The 
amount  of  expansion  varies  with  different 
substances,  but  for  a  given  solid  it  is  directly 
proportional  to  the  temperature. 


Demonstration.  —  Set  up  the  apparatus  shown  in  Fig.  243,  in 
which  the  copper  tube  A B  is  fixed  to  the  support  at  the  point  A,  and 
note  both  the  temperature  of  the  room  and  the  reading  of  the 
pointer.  Cover  the  copper  tube  with  a  non-conductor,  attach  a 
rubber  tube  to  either  end,  and  send  steam  through  it  from  a  boiler. 

After  the  steam  has  been  coming  through  the  tube  freely  for 
some  time,  take  a  second  reading  of  the  pointer  and  call  the  tem- 
perature of  the  steam  100°  C. 

From  the  above  readings  the  changes  in  length  of  the  tube 
and  the  changes  in  its  temperature  can  be  found.  Then  we 
can  write  the  following: 


260  HEAT 

The  change  in  length  of  AB  -1,11? 

r—     — v—  -  =  1  he  change  in  length  for  1 

The  change  in  temperature 

degree. 

The  change  in  length  for  1  degree 

- — ^r — — n 7T — e   AT>       -  —  The  expansion  of  unit 

The  original  length  of  AB 

length  for  1  degree,  and  this  is  the  coefficient  of  linear  expansion. 

In  general :  The  new  length  =  The1  original  length  +  The 
increase  in  length,  or  L'  =  L  +  ktL9 

or  Lf  =  L(l  +  to),  (48) 

in  which  L  is  the  length  of  the  rod  at  zero,  L'  is  its  length  at 
the  temperature  t°,  and  k  is  the  coefficient  of  linear  expansion. 

TABLE  OF  COEFFICIENTS  OF  LINEAR  EXPANSION 

Invar1 0.00000087  Railroad  Steel    .  .  0.00001320 

Pine 0.00000608  Copper      .    .*  .  .  0.00001718 

White  Glass.     .     .  0.00000861  Brass    .     .  '.     ,  .  0.00001878 

Platinum  \  ...     .  0.00000884  Aluminum      .     .  .  0.00002313 

Cast  Iron     .     .     .  0.00001125  Ice   ..'..-.  .  0.00006400 

279.  Effects  of  Expansion  in  Solids.  —  The  difference  in 
temperature  between  the  coldest  winter  days  and  the 
hottest  days  of  summer  is  enough  to  make  a  perceptible 
change  in  the  length  of  long  pieces  of  metal.  Telephone  and 
telegraph  wires  sag  more  in  summer  than  in  winter..  Sus- 
pension bridges,  like  the  Brooklyn  Bridge,  are  several  inches 
higher  in  the  middle  in  midwinter  than  in  summer.  Bridge 
work  and  steam  boilers  are  put  together  with  red-hot  bolts, 
so  that  the  parts  may  be  more  firmly  held  together  when  the 
bolts  are  cool. 

The  table  shows  that  the  coefficients  of  expansion  of  glass 
and  platinum  are  yearly  the  same.  It  is  for  this  reason, 


A  nickel-steel  alloy  containing  36%  of  nickel. 


EXPANSION,   FUSION,  AND  VAPORIZATION         261 


-o- 


B' 


-o- 


and  because  platinum  does  not  oxidize,  that  this  metal 
is  used  as  the  sealed-in  wire  in  incandescent  lamps.  A 
substitute  for  platinum  for  this  purpose  can  be  made  by 
using  a  compound  wire,  the  core  of  which  is  a  nickel-steel 
alloy,  over  which  is  a  thin  sheathing  of  copper.  This  com- 
pound wire  has  a  coefficient  of  expansion  slightly  less  than 
that  of  platinum.  As  it  is  less  expensive,  it  is  generally  used 
in  place  of  platinum.  p 

A  thermostat  is  an  example  of  the  ap- 
plication of  the  unequal  expansion  of 
metals  (Fig.  244).  A  compound  bar  of 
copper  and  iron  is  fixed  at  one  end  and 
free  to  move  at  the  other.  When  the 
temperature  rises  the  point  P  completes 
the  circuit  through  the  cell  C  and  the 
bell  B.  When  the  temperature  falls  the 
circuit  is  made  through  B'.  By  choosing 
bells  of  a  different  tone  it  is  easy  to  tell 
whether  a  room,  a  greenhouse  for  ex- 
ample, is  too  hot  or  too  cold.  If  electro- 
magnets are  substituted  for  the  bells,  they 
can  be  made  to  open  and  close  the  door  that  controls  the 
draft  of  a  furnace,  so  that  the  device  automatically  regu- 
lates the  temperature. 

280.  Cubical  Expansion.  —  When  a  solid  body  expands, 
it  expands  in  all  directions.  If  the  form  of  the  body  is  a 
cube  and  the  length  of  each  edge  at  zero  temperature  is 
1,  the  length  after  expansion  will  be  U  =  1  +  Kt.  The 
volume  at  f  will  be  (1  +  Kt)*  =  1  +  3  Ki  +  3  K2t2  +  #¥. 
Since  K  is  an  extremely  small  fraction,  as  is  seen  from  the 
table,  the  second  and  third  powers  of  A"  Tire  fractions  so  small 
that  the  terms  3  K2t2  and  K3f'  can  be  neglected,  and  the  vol- 


FIG.  244 


262 


HEAT 


ume  is  considered  equal  to  1  +  3  Kt.  Hence  the  coefficient  of 
cubical  expansion,  or  the  fraction  of  its  volume  at  zero  tem- 
perature that  a  body  expands  on  being 
heated  1°  C.,  is  considered  to  be  three 
times  the  coefficient  of  linear  expansion. 

The  coefficient  of  cubical  expansion  of  iee  is 
0.000192;  compare  this  with  its  linear  ex- 
pansion. 

231.  The  Expansion  of  Water.— Dem- 
onstration. —  Fill  the  bulb  A,  Fig:  245,  with 
water  at  4°  C.,  up  to  the  zero  mark  on  B,  at 
which  point  the  volume  of  the  bulb  is  100  c.c. 
Close  C  and  warm  the  water  in  the  beaker  to 
the  temperature  t°  C. 

Both  the  glass  and  the  water  expand,  but 
the  expansion  of  the  water  being  much  greater 
than  the  expansion  of  the  glass,  it  rises  in  the 
calibrated  tube.  The  amount  of  the  expansion 
at  t°  in  cubic  centimeters,  divided  by  the  prod- 
uct of  100  c.c.  X  (t  —  4)  will  give  the  average  apparent  expansion  of 
water  in  glass  per  degree  for  the  range  of  temperature  tested. 

The  temperature  4°  is  taken  as  a  basis  in  the  determination 
of  the  apparent  expansion  of  water,  because  at  that  tempera- 
.ture  water  has  its  smallest  volume  and  maximum  density. 
The  liquid  water  expands  not  only  when  its  temperature  is 
raised  above  4°,  but  also  when  its  temperature  is  lowered 
below  4°.  In  the  latter,  which  is  known  as  its  anomalous 
expansion,  water  differs  from  other  liquids.  When  winter 
approaches,  the  water  of  ponds  and  lakes  becomes  colder  at 
the  surface  and  sinks,  setting  up  convection  currents,  so  that, 
before  the  water  at  the  surface  becomes  colder  than  4  °,  the 
entire  body  of  water  is  of  the  uniform  temperature  of  4°. 
Were  it  not  for  the  anomalous  expansion  of  water,  this  process 


FIG.  245 


EXPANSION,  FUSION,  AND  VAPORIZATION      263 


E:ri^r=^£--— ji^==zrr^^r^r.z£a  — =====.-====1 


FIG.  246 


would  continue  down  to  the  freezing  point.  This  expansion, 
however,  stops  the  convection  currents,  and  when  freezing 
begins,  the  water  quite  ' 

:__ 

near  the  top  is*  the  only    • 
part  that  is  colder  than  4°, 
hence  fish  that  are  under 
the^  ice  are  in  water  of  an 
almost    uniform   tempera- 


ture. 

Since  the  change  in  vol- 
ume per  degree  is  very  small,  it  is  best  shown  by  a  curve  in 
which  the  scale  of  volumes  is  taken  very  large.     In  Fig.  247 

each  division  in  the  vertical 
scale  represents  0.00005  of 
the  volume  at  4°. 

The  expansion  of  water  is 
not  uniformly  proportional 
to  the  temperature.  As  we 
go  from  4°  in  either  direction, 
the  amount  of  expansion  per 
degree  constantly  increases* 
From  4°  to  5°  the  expansion 
is  0.000008  of  the  volume  at 
4°  ;  from  14°  to  15°,  0.000146 ; 
from  24°  to  25°,  0.000253- 
Liquids  in  general  have  dif- 
ferent rates  of  expansion  at 

F,G.247.-ExpanSion  of  Water        ^^     temperatures .      jn 

this  they  differ  from  solids  and  gases,  which  expand  uniformly. 


1.00200 


1.00175 


1.00150 


1.00125 
en 
U 

|  1.00100 


1.00075 


1.00050 


1.00025 


1.00000 


5°       10°      15°       20° 

TEMPERATURES, 
in  Centigrade  Degrees. 


The  rate  of  expansion  of  mercury,  however,  is  nearly  uniform. 
Its  coefficient  of  cubical  expansion,  for  temperatures  near  zero,  is 
0.0001818. 


264 


HEAT 


282.  The  Measurement  of  Expansion  of  Gases.  —  The 

varying  volume  of  the  air  in  an  air  thermometer  shows 
that  a  gas  expands  when  heated,  but  it  does  not  show  the 
amount  of  the  change  in  volume  per  degree. 
There  are  two  conditions  under  which  the 
effect  of  heat  on  a  gas  can  be  measured. 
If  the  gas  is  heated  and  the  pressure  kept 
constant,  we  can  measure  the  change  in 
its  volume;  and  if  the  gas  is  heated  and 
the  volume  kept  constant,  we  can  measure 
the  change  in  its  pressure. 

Measurements   under  both    these   conditions 
can  be  made  by  the  use  of  an  air  thermometer 
such  as  is  shown  in  Fig.  248.     In  measurements 
FIG.  248  under  constant  volume  the  mercury  in  the  left- 

hand  column  is  kept  at  a  fixed  height  by  raising 
or  lowering  the  right-hand  column,  and  in  measurements  under 
constant  pressure  the  mercury  level  is  kept  at  the  same  height 
in  both  columns  by  the  same  means. 

As  a  result  of  such  measurements  it  is  found  that  for  each 
degree  of  change  in  the  temperature  of  a  gas  under  constant 
pressure  there  is  a  change  in  its  volume  equal  to  ^y?  of  its 
volume  at  zero.  Since  this  is  true  of  all  other  gases  as  well 
as  of  air,  we  can  write  273-  or  0.003665  as  the  uniform  coeffi- 
cient of  expansion  of  all  gases. 

283.  Absolute  Zero.  —  If  a  given  mass  of  gas  with  a 
volume  of  273  c.c.  at  zero  is  steadily  cooled,  its  volume  will 
be  263  c.c  at  -  10°,  253  c.c.  at  -  20°,  and  so  on.     The 
logical  conclusion  would  be  that  if  the  temperature  were 
reduced  to   —  273°  the  volume  of  the  gas  would  be  zero. 
Before  reaching  that  temperature,  however,  gases  change  into 
liquids.    The  temperature  —  273°  is  called  the  absolute  zero, 


EXPANSION,   FUSION,  AND   VAPORIZATION       265 

and  temperatures  based  upon  this  temperature  as  0°  are 
called  absolute  temperatures  and  expressed  as  degrees  Kelvin. 
Thus  20°  C.  =293°  K.  Gases  are  liquefied  by  increasing 
the  pressure  and  reducing  the  temperature,  and  by  the 
evaporation  of  liquid  helium  under  reduced  pressure  the 
temperature  has  been  brought  as  low  as  —  270°. 

284.  The  Law  of  Charles.  —The  discovery  that  all  gases 
are  subject  to  the  same  law  governing  the  relation  of  volume 
and  temperature  at  constant  pressure,  was  made  by  Professor 
Charles  of  Paris.     The  law  which  has  received  his  name  may 
be  stated  as  follows : 

Under  a  constant  pressure  the  volume  of  a  given  mass  of  gas 
is  proportional  to  its  absolute  temperature. 

285.  Combination  of  Boyle's  Law  with  the  Law  of  Charles. 

Let  V  =  the  volume  and  P  the  pressure  of  a  gas  at  f. 
Let  V  —  its  volume  and  P'  its  pressure  at  t'°. 
Let  V\  —  its  volume  at  the  pressure  P'  and  temperature  f. 
Then  by  Boyle's  law  PV  =  P'V\,  since  the  temperature 
is<°. 

Vl      V 
By  the  law  of  Charles  y  =  "TV  since    the  pressure  is  P', 

T  and  T'  being  absolute  temperatures  corresponding  to  t° 
and  t'°  respectively. 

Multiplying  these  equations  term  by  term  we  get,  by  elimi- 

PV      P'V 

natmg  Vi,  -y  =  ~^r '  (49) 

This  formula  is  used  in  the  solution  of  such  questions  as 
the  following : 

EXAMPLE.  —  The  volume  of  a  gas  at  22°  C.  and  760  mm.  pressure 
is  50  c.c.    What  will  it  be  when  the  temperature  is  raised  to  100°  C. 


266  HEAT 

and  the  pressure  is  700  mm.  ?    Since  T  is  the  absolute  temperature, 
substitution  in  the  formula  gives 

760  x  50       700  x  V 


273  +  22       273  +  100, 
whence  F'  =  68.8  c.c. 

286.  Effects  of  Expansion  in  the  Air.  —  The  effect   of 
heat  upon  air  may  be  seen  in  the  currents  that  are  set  up 
near  a  heated  surface.     The  air  next  the  surface  becomes 
warmer  and  lighter,  and  cooler  air  displaces  it.     This  sets 
up  an  ascending  current  over  the  heated  area,  and  a  hori- 
zontal current  at  near-by  places.     If  this  heated  surface  is 
an  extensive  tract  of  the  earth,  the  result  will  be  the  setting 
up  of  violent  winds  toward  it. 

Just  as  the  temperature  of  air  is  raised  by  compression 
(§  260),  so  also  it  is  lowered  by  expansion  against  reduced 
pressure.  The  ascending  current  over  the  heated  surface 
rises  to  an  altitude  where  the  atmospheric  pressure  is  con- 
siderably less.  Because  of  the  resulting  expansion  of  this 
air,  the  temperature  is  likely  to  fall  so  low  as  to  cause  the  con- 
densation of  its  water  vapor  into  clouds  and  rain. 

The  beginning  of  a  thunderstorm  exemplifies  both  these  effects. 
Use  is  made  of  the  second  effect  in  liquefying  air  and  other  gases. 
The  pressure  on  highly  compressed  cold  air  is  suddenly  reduced,  and 
the  resulting  expansion  of  part  of  the  air  withdraws  so  much  heat 
from  the  rest  that  the  residue  is  liquefied. 

287.  Changes  of  Physical  Condition.  —  If,  when  the  tem- 
perature is  several  degrees  below  zero,  a  piece  of  ice  is  brought 
into  a  warm  room,  its  temperature  rises  until  it  is  at  zero. 
If  now  more  heat  is  applied  to  it,  it  melts  to  a  liquid,  then 
heats  to  100°,  and  then  boils  away.     In  the  course  of  this 
process  there  has  been  one  change  of  the  body  from  a  solid 


EXPANSION,  FUSION,  AND  VAPORIZATION      267 


FIG.  249 


to  a  liquid,  and  another  from  a  liquid  to  a  vapor.  A  similar 
change  of  physical  condition  can  be  brought  about  with  most 
solid  bodies  if  only  the  proper  change  of 
temperature  can  be  produced. 

288.  Fusion.  —  Demonstration.  —  Draw 

out,  a  piece  of  glass  tubing  until  its  inner 
diameter  is  1  mm.  cr  less,  and  close  the  end. 
Drop  into  the  open  end  a  small  piece  of  bees- 
wax and  hold  the  tube  in  a  flame  until  the 
wax  is  melted.  Let  it  solidify  at  the  closed 
end.  Tie  the  tube  to  a  thermometer  as  shown 
in  Fig.  249.  Put  the  thermometer  and  tube 
into  a  beaker  of  water  and  heat  it  until  the 
wax  melts.  Take  the  temperature  of  melt- 
ing, remove  the  source  of  heat,  and  again  read 
the  thermometer  at  the  instant  that  the  wax  begins  to  solidify. 
Take  the  mean  of  the  two  readings  as  the  melting  point  of  the  wax. 

The  change  from  a  solid  to  a  liquid  as  a  result  of  the  appli- 
cation of  heat  is  called  fusion,  or  melting.  The  temperature 
at  which  a  solid  melts  is  called  its  melting  point.  The  laws 
effusion  are  as  follows : 

I.  Every  solid  having  a  crystalline  structure  begins  to  melt 
at  a  certain  fixed  temperature  that  is  always  the  same  for  that 
substance  if  the  pressure  is  constant. 

II.  The  temperature  of  a  melting  solid  remains  unchanged 
from  the  time  melting  begins  until  the  body  is  entirely  melted. 

TABLE  OF  AVERAGE  MELTING  POINTS 


Alcohol  .... 
Mercury.  .  .  . 
Ice  

-130.50° 
-  39.04° 
0° 

Lead      .     .     . 
Silver     .     .     . 
Copper  . 

326° 
950° 
1100° 

White  wax  .  .  . 
Sulphur.  .  .  . 

65° 
115.1° 

*^/\S£S£S\S*.          • 

Iron  .... 
Platinum    .     . 

1500° 
1900° 

268  HEAT 

289.  Solidification  is  the  reverse  of  fusion,  and  takes  place 
when  a  liquid  is  cooled  below  its  melting  point.    The  temper- 
ature at  which  any  substance  solidifies  is  the  same  as  the 
melting  point,  and  for  some  substances,  as  water  and  mercury, 
this  temperature  is  called  the  freezing  point.     Every  liquid 
in  freezing  gives  off  an  amount  of  heat  equal  to  that  which 
would  be  required  to  melt  it  if  frozen.      The  freezing  point 
of  vegetables  is  a  little  lower  than  the  freezing  point  of  water. 
For  this  reason  pans  of  water  are  sometimes  placed  in  vege- 
table cellars,  in  order  that  the  water,  while  freezing,  may 
give  out  heat  enough  to  keep  the  air  above  the  freezing 
point  of  the  vegetables. 

Most  liquids  shrink  on  solidifying;  but  water,  on  the 
contrary,  expands.  Water  expands  so  that  917  c.c.  of 
water  becomes  1000  c.c.  of  ice.  Were  it  to  decrease  in 
volume  instead,  the  crystals  of  ice  forming  at  the  surface 
of  a  lake  would  sink,  and  during  a  cold  winter  the  water 
would  become  solid  ice  from  the  bottom  to  the  top. 

Demonstration.  —  Fill  with  water  an  air  thermometer  bulb  with 
a  long  stem,  and  pack  the  bulb  in  a  freezing  mixture.  The  water  in 
the  stem  will  be  seen  gradually  to  sink,  then  to  turn  and  rise,  indicat- 
ing that  the  minimum  volume  has  been  passed,  and  then  suddenly 
to  rise  again.  On  taking  the  bulb  out  afiter  some  minutes  it  will  be 
found  broken,  and  the  water  will  be  a  ball  of  ice. 

290.  Effect  of  Pressure  on  the  Freezing  Point.  — The 
effect  of  increased  pressure  on  the  freezing  point  of  water  is 
seen  in  the  following : 

Demonstration.  —  Place  a  block  of  ice  on  a  suitable  support 
and  put  over  it  a  piece  of  wire  with  a  heavy  weight  at  each  end. 
This  brings  pressure  upon  the  ice  directly  under  the  wire  and  it 
will  melt.  As  the  wire  sinks  in  the  ice  the  melted  water  above  it, 


EXPANSION,  FUSION,  AND  VAPORIZATION      269 

being  freed  from  pressure,  freezes  again  and  finally  the  wire  will 
cut  entirely  through  the  ice,  which  will  still  remain  as  a  single 
block. 

This  thawing  and  freezing  of  ice  under  great  changes  of  pressure 
is  seen  in  a  large  scale  in  glaciers,  their  constant  flow  down  a 
slope  being  dependent  on 
this  action. 

291.  A  Freezing  Mix- 
ture   can    be    made    by 
mixing    1    part    of   salt 
with  3  parts  of  snow  or 
cracked  ice.     The  ice  in 
contact  with  the  salt  is 
melted,  the  heat  neces- 
sary   for    the    melting 

being  withdrawn  from  the  objects  near  by.  The  salt  is  dis- 
solved, and  the  temperature  falls  to  the  freezing  point  of 
the  salt  solution,  which  is  lower  than  that  of  water.  Other 
salts  mixed  with  ice  or  snow  will  give  lower  temperatures, 
as  calcium  chloride,  for  example.  When  this  salt  is  mixed 
with  snow  in  the  proportion  of  3  parts  of  the  salt  to  2  parts 
of  snow,  it  will  give  a  temperature  low  enough  to  freeze 
mercury. 

292.  Vaporization.  —  As  the  molecules  of  water  (or  ice) 
in  their  vibration  (§  243)  strike  against  the  surface,  many 
of  them  force  their  way  through  it  and  pass  into  the  air, 
where  they  exist  as  molecules  of  water  vapor.     When  heat 
is  applied,  the  temperature  is  raised,  which  means  that  the 
velocity  of  the  molecules  is  increased;  and  the  number  of 
molecules  that  pass  into  the  air  increases  with  their  velocity. 
As  long  as  the  temperature  is  below  the  boiling  point,  the  pro- 
cess is  called  evaporation. 


270  HEAT 

293.  Laws  of  Evaporation. 

I.  Evaporation  increases  with  the  temperature.     Evapora- 
tion takes  place  even  at  very  low  temperatures.     A  block 
of  ice  left  for  a  few  days  in  a  place  where  the  temperature 
is  below  zero  will  lose  a  considerable  amount  by  evapora- 
tion.    Wet  clothes  hung  out  on  a  cold  winter  day  will  freeze 
at  once,  but  will  soon  become  dry. 

II.  Evaporation  increases  if  the  surface  of  the  liquid  is 
increased.     Recent  experiments  show  that  evaporation  is 
not  directly  proportional  to  the  extent  of  the  surface.     Evap- 
oration takes  place  more  rapidly  near  the  boundaries  of  a 
surface  than  at  the  center,  and  in  the  case  of  two  circular  sur- 
faces the  evaporation  is  nearly  proportional  to  the  respective 
circumferences. 

III.  Evaporation  is  inversely  proportional  to  the  pressure 
upon  the  liquid. 

IV.  Evaporation  decreases  as  the  air  becomes  saturated. 

Air  is  said  to  be  saturated  with  moisture  when  it  will  hold 
no  more  at  the  given  temperature.  If  the  temperature  is 
raised,  more  evaporation  can  take  place,  but  if  it  is  lowered, 
condensation  will  take  place;  that. is,  some  of  the  vapor  will 
be  changed  back  to  tiny  water  drops  or  ice  crystals.  At  any 
given  temperature  the  amount  of  vapor  necessary  for  satura- 
tion is  always  the  same  per  cubic  meter  of  space,  no  matter 
how  much  air  is  also  in  that  space. 

If  the  space  into  which  evaporation  takes  place  is  inclosed 
and  the  air  is  removed,  the  evaporation  takes  place  rapidly, 
and  saturation  is  quickly  reached.  If  the  air  is  not  removed, 
the  evaporation  takes  place  much  more  slowly,  because  the 
air  molecules,  striking  upon  the  surface  of  the  water,  cause 
a  pressure  upon  the  surface  and  oppose  the  molecules  that 


EXPANSION,   FUSION,  AND  VAPORIZATION       271 


NUMBER  OF  GRAMS  OF  MOISTURE  NEEDED  FOR  SATURATION  PER 
CUBIC  METER  AT  VARIOUS  TEMPERATURES  C. 


-10° 

2.363  g. 

5° 

6.761  g. 

20° 

17.118  g. 

-  9° 

2.546 

6° 

7.219 

21° 

18.143 

-  8° 

2.741 

7° 

7.703 

22° 

19.222 

7° 

2.949 

8° 

8.215 

23° 

20.355 

-  6° 

3.171 

9° 

8.757 

24° 

21.546 

-  5° 

3.407 

10° 

9.330 

25° 

22.796 

-  4° 

3.659 

11° 

9.935 

26° 

24.109 

-  3° 

3.926 

12° 

10.574 

27° 

25.487 

-  2° 

4.211 

13° 

11.249 

28° 

26.933 

-  1° 

4.513 

14° 

11.961 

29° 

28.450 

0° 

4.835 

15° 

12.712 

30° 

30.039 

1° 

5.176 

16° 

13.505 

31° 

31.704 

2° 

5.538 

17° 

14.339 

32° 

33.449 

3° 

5.922 

18° 

15.218   i 

33° 

35.275 

4° 

6.330 

19° 

16.144 

34° 

37.187 

are  coming  from  the  liquid.  In  the  first  case  the  final  pres- 
sure is  that  of  the  saturated  vapor  alone.  In  the  second 
case  it  is  that  of  the  air  plus  that  of  the 
saturated  vapor.  The  effect  of  atmospheric 
pressure  upon  the  rate  of  evaporation  is  so 
great  that  the  moisture  present  in  the  air 
is  generally  much  less  than  that  required 
for  saturation. 


294.  The    Dew-point.  —  Demonstration.  — 

Pour  ether  into  a  test  tube  until  it  is  half  full, 
and  put  a  thermometer  into  it.  Bend  a  tube  at 
right  angles  and  place  in  the  test  tube  as  in  Fig. 
251.  Connect  the  short  end  with  a  long  rubber 
tube  and  blow  gently  through  the  ether.  The 
ether  will  evaporate  and  the  temperature  will 
rapidly  fall.  Watch  the  surface  of  the  lower  end 


FIG.  251 


272  HEAT 

of  the  test  tube  and  take  the  reading  of  the  thermometer  when 
moisture  first  appears  on  the  outside.  Now  stop  blowing  through 
the  ether,  and  its  temperature  will  rise.  Take  a  second  reading  of 
the  thermometer  when  the  moisture  disappears.  The  average  of 
the  two  readings  will  be  the  dew-point. 

The  dew-point  is  the  temperature  to  which  air  must  be  low- 
ered so  that  the  vapor  present  will  be  enough  for  saturation. 

Fogs,  clouds,  rain,  and  snow  result  from  a  lowering  of  the 
temperature  of  the  air  below  the  dew-point.  The  most 
oppressive  days  in  summer  are  those  in  which  the  air  is  nearly 
saturated  with  water  vapor. 

295.  Humidity  of  the  Air.  —  The  relative  humidity  of  the 
air  is  the  ratio  between  the  amount  of  moisture  present  in  the 
air  and  the  amount  that  would  be  present  if  the  air  were  satu- 
rated. 

If  the  temperature  of  the  air  is  taken  at  the  same  time 
that  the  dew-point  is  determined,  the  relative  humidity  can 
be  found  by  the  help  of  the  table  in  §293.  Suppose,  for 
example,  that  at  a  time  when  the  temperature  of  the  air  is 
23°  C.  the  dew-point  is  17°  C.  From  the  table  the  amount 
of  moisture  present  when  the  air  is  saturated  at  17°  C.  is 
14.339  g.  per  cubic  meter.  But  at  its  temperature  of  23°  C. 
it  could  contain  20.355  g. ;  hence  the  relative  humidity  is 
14.339  :  20.355,  or  about  70  per  cent. 

Instruments  used  in  determining  relative  humidity  are  called 
hygrometers.  The  wet-and-dry-bulb  hygrometer  consists  of  two 
similar  thermometers,  the  bulb  of  one  being  covered  with  a  wick, 
the  end  of  which  dips  into  water.  This'keeps  the  covering  of  the 
bulb  wet,  and  the  rate  of  evaporation  affects  the  temperature  of  the 
bulb.  If  there  is  little  moisture  in  the  air,  the  evaporation  takes 
place  rapidly,  and  the  wet-bulb  thermometer  will  read  considerably 
lower  than  the  other.  Tables  are  provided,  by  the  use  of  which  the 
relative  humidity  can  be  determined  from  the  readings.  - 


EXPANSION,   FUSION,  AND  VAPORIZATION      273 


296.  Boiling.  —  If  a  quantity  of  fresh  water  is  placed  over 
a  source  of  heat,  the  first  effect  will  be  the  gathering  of  air 
bubbles  on  the  sides  of  the  dish.  This  comes  from  the  air 
dissolved  in  the  water.  After  a  time  these  bubbles  break 
away  from  the  sides  and  bottom  and  rise  to  the  surface.  All 
this  time  the  temperature  of  the  water  has  been  rising,  which 
means  that  the  velocity  of  the  molecules  within  the  liquid 
has  been  increasing.  As  this  velocity  increases  the  number 
of  impacts  of  the  molecules  up  against  the  surface  of  the  water 
increases  and  there  is  a  more  rapid  escape  of  water  molecules 
into  the  air.  A  point  is  soon  reached 
when  the  escape  of  these  molecules  in 
the  form  of  steam  is  very  rapid;  the 
temperature  now  stops  rising  and  the 
liquid  is  said  to  boil.  Boiling  is  also 
called  ebullition. 


Demonstrations.  — Heat  water  in  a  beaker 
to  about  50°  and  remove  the  flame.  Fill  a  test 
tube  half  full  of  ether,  insert  a  thermometer, 
and  put  them  into  the  hot  water,  as  in  Fig. 
252.  Stir  the  water  in  the  beaker  with  the 
test  tube,  and  take  the  lowest  temperature  at 
which  the  ether  boils,  as  its  boiling  point. 


FIG.  252 


NOTE. — Aflame  must  not  be  brought- near  the  ether,  as  its 
vapor  is  very  inflammable. 

Make  a  similar  experiment  with  alcohol  and  find  its  boiling 
point. 

Fill  a  round-bottomed  flask  half  full  of  water.  Boil  this  over  a 
Bunsen  burner,  and  when  steam  is  coming  freely  from  the  neck,' 
remove  the  burner  and  put  a  stopper  in  the  mouth  of  the  flask. 
Invert  the  flask  in  a  ring  support,  as  shown  in  Fig.  253,  and  pour  cold 
water  over  it.  This  will  condense  the  vapor  above  the  water  and 
reduce  the  pressure  upon  its  surface.  As  a  result  the  water  will 

Rev. 


274 


HEAT 


begin  to  boil  vigorously,  showing  that  if  the  pressure  is  reduced  the 
boiling  point  is  lowered. 

The  effect  of  reduced  pressure  upon  the  boiling  point  is 

seen  upon  high  mountains,  where 
water  boils  at  so  low  a  temper- 
ature that  food  cannot  be  cooked 
by  boiling.  Advantage  is  taken 
of  this  effect  in  the  making  of 
sugar,  where  vacuum  pans  are 
used  to  evaporate  the  solution 
without  burning  it.  In  the  ex- 
traction of  glue  from  bones  and 
hides  the  pressure  is  increased 
and  the  boiling  point  correspond- 
ingly raised. 


FIG.  253 


297.  The  Spheroidal  State.  —  Whenever  water  is  thrown 
upon  a  very  hot  metallic  surface,  a  condition  called  the 
spheroidal  state  is  set  up.  The  effect  of  the  heated  surface 
is  to  vaporize  a  little  of  the  liquid,  so  that  the  remainder 
does  not  rest  directly  upon  the  metal,  but  upon  a  cushion 
of  steam.  This  by  its  constant  movement  keeps  the  liquid 
in  rapid  vibration.  The  liquid  takes  the  globular  form  be- 
cause of  surface  tension,  and  changes  into  vapor  at  a  rate 
faster  than  evaporation  and  slower  than  boiling.  If  the 
metal  cools  and  the  liquid  comes  in  contact  with  it,  a  sudden 
production  of  steam  is  the  result.  Steam  boiler  explosions 
have  resulted  from  the  water  in  the  boiler  getting  low,  and 
then  cold  water  being  suddenly  turned  on  after  the  boiler 
had  become  red-hot  above  the  water  line. 


Demonstration.  —  Place  a  smooth  tin  or  brass  plate  upon  a  tripod 
and  heat  it  with  a  burner.     Drop  a  few  drops  of  water  upon  it  with 


EXPANSION,  FUSION,  AND  VAPORIZATION      275 

a  pipette.  After  the  spheroidal  condition  is  set  up,  remove  the  flame 
and  let  the  plate  cool.  What  occurs  when  the  water  touches  the 
plate?  Why? 

298.  Condensation  of  Vapors ;  Distillation.  —  The  conden- 
sation of  a  vapor  to  a  liquid  is  brought  about  by  lowering 
its  temperature  or  by  increasing  the  pressure  upon  it,  or  by 
both.  In  condensing,  it  gives  off  as  much  heat  as  was  re- 
quired to  vaporize  it.  It  is  possible  to  separate  a  liquid 


FIG.  254 

from  substances  with  which  it  is  mixed,  or  which  it  holds 
in  solution,  by  boiling  the  mixture  or  solution  and  condensing 
the  vapor.  This  process,  which  depends  upon  the  difference 
in  the  boiling  point  of  liquids,  is  called  distillation,  and  the 
liquid  that  has  been  purified  by  it  is  called  the  distillate. 
The  condenser,  in  which  the  condensation  takes  place,  may 
be  in  the  form  of  a  straight  tube,  as  in  Fig.  254,  or  in  the  form 
of  a  spiral  tube,  which  is  called  a  worm.  Each  form  is  sur- 
rounded by  a  water  jacket  to  keep  the  tube  cool.  The  purity 
of  the  distillate  is  increased  by  redistillation.  In  a  mixture 


276  HEAT 

of  alcohol  and  water,  for  example,  a  little  water  comes 
over  with  the  alcohol  in  the  first  distillation,  but  less  in 
the  second. 

Demonstration.  —  Arrange  apparatus  as  shown  in  Fig.  254. 
Pass  cold  water  in  at  the  lower  end  of  the  water  jacket  and  let  it  run 
out  at  the  top.  Put  a  mixture  of  equal  parts  of  alcohol  and  water 
in  the  flask.  Boil  it  until  about  a  third  of  the  mixture  is  condensed 
in  the  beaker.  Remove  the  flame  and  test  the  distillate  by  setting 
it  on  fire.  Test  the  mixture  remaining  in  the  flask  in  the  same  way. 

299.  Fractional  Distillation.  —  Since  every  liquid  has  its 
own  boiling  point,  it  is  possible  to  separate  a  mixture  of 
several  that  have  different  boiling  points,  by  the  process 
called  fractional  distillation.     When  crude  petroleum  is  dis- 
tilled, as  soon  as  the  boiling  begins  it  is  kept  at  the  same 
temperature  until  no  more  distillate  comes  over.     This  most 
volatile  part  of  the  oil  having  been  removed,  the  temperature 
is  now  raised  a  few  degrees,  boiling  begins  again,  and  the 
petroleum  is  kept  at  the  new  temperature  as  long  as  any 
vapor  comes  over.     The  process  is  repeated   a  number  of 
times.     The  product  that  comes  off  last  is  the  highest  grade 
of  all.     That  is  it  ignites  at  the  highest  temperature. 

When  air  is  liquefied  and  allowed  to  stand  in  a  flask,  the 
nitrogen  will  boil  off  first,  since  the  boiling  point  of  nitrogen 
is  -  195°,  while  that  of  oxygen  is  -  183°.  After  the  flask 
has  stood  for  some  time,  the  nitrogen  will  have  boiled  away 
and  the  liquid  left  will  be  oxygen. 

300.  Critical  Temperature.  —  The  pressure  required  to  re- 
duce a  gas  to  a  liquid  increases  as  the  temperature  rises. 
Moreover,  there  is  for  every  gas  a  temperature  above  which 
it  cannot  be  liquefied,  however  great  the  pressure.     This 
temperature  is  called  the  critical  temperature. 


EXPANSION,  FUSION,  AND  VAPORIZATION      277 


SUBSTANCE 

BOILING  POINT 
(pressure  =  760  mm.) 

CRITICAL 
TEMPERATURE 

Water       
Alcohol                                   .     , 

+  100°  C. 

786 

+  365°  C. 
243° 

Ether    

38° 

190° 

Ammonia-     
Carbon  dioxide 

-    33° 

—    78° 

130° 
31° 

Oxygen     
Air 

-  183° 
-  191° 

-  118° 
—  140° 

Nitrogen 

-  195° 

—  146° 

Hydrogen      .    .     . 

-  253° 

-  235° 

Helium     .    .    

-  268.6° 

-  268° 

Figure  255  is  a  graphical  representation  of  the  relation 
between  the  pressure,  tempera- 
ture, and  physical  state  of  am- 
monia.1 This  shows  that  ammo- 
nia can  be  reduced  from  a  gas 
to  a  liquid  by  pressures  varying 
from  115  atmospheres  at  the 
critical  temperature,  130°,  to  1 
atmosphere  when  the  tempera- 
ture is  reduced  to  -  33°.  It 
also  shows  that  ammonia  can 
be  reduced  to  a  liquid  at  the 
ordinary  temperature  of  the  air 
by  pressure  alone. 

301.  Manufactured  Ice.  —  In 
the  making  of  manufactured  ice, 

1  Sometimes  called  ammonia  gas. 
The  liquid  "  ammonia  "  in  common 
use  is  really  ammonia  water;  that 
is,  water  that  has  absorbed  much  am- 
monia. 


PRES-       TEMPER-        PHYSICAL 

SURE       ATURE,C.          STATE 

*I< 

V      Always  a  GAS 

CL    I 

_           I 

>  130° 

- 

Critical  Tem- 
perature 

• 

.C 

- 

A  GAS  or 

ll< 

0)   ^_ 

— 

I      a  LIQUID, 
f     dependent 

£o 

- 

on  pressure 

£ 

~ 

£ 

T 

If. 

0° 

S-33J 

fe.W 

Boiling  Point 

I  A  LIQUID 

—77°  h  <~x freezing  Point 

A  SOLID 

FIG.  255  —Physical  State  of 
Ammonia 


278 


HEAT 


the  water  to  be  frozen  is  poured  into  cans  set  in  a  large  tank 
containing  brine  (Fig.  256).  Coils  of  pipe  are  placed  in  the 
tank,  and  in  these  coils  ammonia  which  has  been  liquefied  by 
pressure  is  allowed  to  vaporize.  The  pressure  is  reduced  by 
pumping  the  ammonia  vapor  back  into  the  compressor.  By 
the  vaporization  of  the  liquid  and  the  rapid  expansion  of  the 
vapor,  the  temperature  of  the  brine  is  lowered  to  about 


1 


FIG.  256 


—  10°  C.  The  freezing  of  the  water  in  the  cans  goes  on 
rapidly,  the  crystals  of  ice  extending  from  all  sides.  The 
heat  produced  in  compressing  and  liquefying  the  ammonia 
is  allowed  to  dissipate  before  the  liquid  ammonia  is  returned 
to  the  coils.  The  cooling  of  the  compressed  ammonia  is 
brought  about  by  causing  cold  water  to  drip  over  the  pipes 
leading  from  the  compression  cylinder,  before  they  connect 
with  the  expansion  cylinder.  This  cools  the  ammonia  before 
it  enters  the  expansion  cylinder  and  thus  secures  a  lower 
temperature  in  the  brine  tank. 


EXPANSION,  FUSION,  AND  VAPORIZATION      279 

Questions 

1.  Why  are  the  bolts  of  an  iron  bridge  put  in  hot? 

2.  What  takes  place  in  the  water  of  a  pond  as  the  weather  grows 
colder  in  the  fall? 

3.  Suppose  a  copper  wire  is  fused  into  a  glass  tube.     What  will 
happen  when  they  cool  down  to  the  temperature  of  the  air  ? 

A.  Does  the  same  thing  happen  if  a  platinum  wire  is  used  ?     Ex- 
plain. 

5.  What  will  happen  if  the  corner  of  a  piece  of  ice  is  held  in  the 
top  of  a  beaker  of  warm  water  ?     The  result  can  be  seen  more  readily 
if  the  water  is  slightly  colored. 

6.  What  takes  place  in  a  beaker  of  water  that  is  being  heated 
over  a  Bunsen  burner  if  the  burner  is  not  under  the  middle  of  the 
beaker  ? 

7.  Is  a  football  tighter  in  warm  weather  or  in  cold?     Which  is 
better,  to  fill  the  ball  by  blowing  with  the  breath  or  to  use  an  air 
pump  ?     Why  ? 

8.  Why  does  decreasing  the  pressure  on  a  given  quantity  of  gas 
increase  its  volume? 

9.  Why  does  heating  it  have  the  same  effect? 

10.  Why  do  water  pipes  burst  when  the  water  in  them  freezes  ? 

11.  Would  increasing  the  pressure  on  ice  at  0°  C.  melt  it  if  the 
water  did  not  expand  on  freezing  ? 

12.  What  is  the  effect  of  placing  a  beaker  of  water  at  80°  C. 
under  the  receiver  of  an  air  pump  and  then  exhausting  the  air? 

13.  Why  does  moisture  collect  on  a  window  pane  in  cool  weather  ? 

14.  Why  is  sea  water  distilled  before  being  used  in  the  boilers  of 
a  steamship  ? 

15.  Why  does  evaporation  take  place  more  slowly  when  the  air 
is  moist? 

16.  Why  do  wet  clothes  freeze  dry  on  a  cold  day  in  winter? 

17.  Why  does  a  wet  road  dry  sooner  if  the  wind  blows  ? 

18.  Why  are  the  cans,  containing  water  to  be  frozen  in  an  ice 
machine,  placed  in  brine  instead  of  in  water? 

19.  Describe  and  explain  the  action  that  takes  place  in  each  part 
of  the  refrigerating  machine  shown  in  Fig.  256  and  state  the  reason 
for  the  direction  of  flow  in  the  pipes. 


280  HEAT 

Problems 

1.  How  much  will  a  steel   rail  30  ft.  long  increase  in  length 
when  the  temperature  changes  from  zero  to  22°  C.  ? 

2.  If  a  metal  rod  150  cm.  long  at  0°  C.  expands  0.24  cm.  on 
being  heated  to  100°  C.,  what  is  its  coefficient  of  linear  expansion? 

3.  How  much  would  a  meter  scale  made  of  invar  expand  on  being 
heated  from  -  20°  C.  to  +  28°  C.? 

4.  The  density  of  ice  is  0.917.     What  will  be  the  volume  of  a 
cubic  foot  of  water  after  freezing? 

6.  A  balloon  contains  4000  cu.  ft. .  of  gas  at  23°  C.     What 
will  be  the  volume  of  the  gas  at  0°  C.  ? 

6.  If  the  volume  of  an  inclosed  body  of  air  is  426  c.c.  at  zero 
what  will  it  be  when  the  temperature  is  raised  to  20°  C.,  the  pressure 
being  the  same? 

7.  If  the  volume  of  a  gas  at  21°  C.  and  a  pressure  of  950  mm. 
of  mercury  is  126  c.c.,  what  will  it  be  at  0°  C.  and  a  pressure  of 
760  mm.  ? 

8.  The  pressure  per  sq.  cm.  on  150  c.c.  of  gas  at  16°  C.  is  3.2  kg. 
What  must  it  be  to  reduce  the  volume  to  120  c.c.  when  the  temper- 
ature is  23°  C.  ? 

9.  The  temperature  of  200  c.c.  of  gas  at  a  pressure  of  760  mm. 
of  mercury  is  21°  C.     What  will  it  be  if  the  volume  is  reduced  to 
150  c.c.  by  a  pressure  of  1140  mm.  ? 

10.  What  would  the  temperature  have  been  in  problem  9,  if 
the  pressure  used  to  reduce  the  volume  of  the  gas  had  been  two 
atmospheres,  or  1520  mm.  ? 

11.  Which  contains  the  greater  amount  of  moisture,  air  at  15°  C. 
having  a  humidity  of  90%  or  air  at  23°  C.  with  a  humidity  of 
60%? 

12.  How  much  moisture  condenses  from  a  cubic  meter  of  air 
that  is  saturated  at  20°  C.  when  the  temperature  falls  to  8°  C.  ? 

13.  On  a  day  when  the  temperature  of  the  air  was  20°  C.  the  dew- 
point  was  found  to  be  11°  C.     What  was  the  relative  humidity? 

14.  If  the  humidity  is  80  %  and  the  temperature  of  the  dew-point 
is  16°  C.,  how  much  moisture  is  in  the  air  per  cubic  meter?     How 
much  would  it  hold  if  saturated,  and  what  was  the  temperature  of 
the  air? 


CALORIMETRY  281 

IV.  CALORIMETRY 

302.  The  Measurement  of  Heat.  —  In  order  to  measure 
the  quantity  of  heat  that  is  given  to  a  certain  amount  of 
water,  two  things  must  be  considered :  the  mass  of  the  water 
and  the  change  of  the  temperature. 

Since  there  are  different  units  of  mass  and  different  ther- 
mometric  scales,  several  thermal  units  are  possible.  The 
two  most  important  are  defined  as  follows :  the  quantity 
of  heat  required  to  raise  1  g.  of  water  through  1°  C.  is  called 
a  calorie;  l  the  quantity  of  heat  required  to  raise  1  Ib.  o'f 
water  through  1°  F.  is  called  a  British  thermal  unit  (B.  T.  U.). 
1  B.  T.  U.  =  252  calories.  The  measurement  of  the  heat 
used  in  changing  either  the  temperature  or  the  physical  con- 
dition of  a  body  is  called  calorimetry. 

303.  Specific  Heat.  —  Demonstration. — Place  50  g.  of  shot 
in  one  test  tube  and  50  g.  of  iron  filings  in  another  similar  tube. 
Raise  both  to  the  same  temperature  by  placing  them  in  a  beaker  of 
hot  water.     Into  each  of  two  small  beakers  pour  100  g.  of  water 
that  has  been  cooled  to  the  zero  point  by  means  of  ice.     Pour  the 
shot  into  one  beaker  and  the  filings  into  the  other.     Take  the  tem- 
perature of  the  water  in  each,  and  it  will  be  found  that  the  filings 
have  given  to  the  water  the  greater  amount  of  heat,  as  is  shown  by 
the  higher  temperature  in  the  beaker  containing  them. 

This  demonstration  shows  that  iron  has  a  greater  amount 
of  heat  than  lead  at  the  same  temperature.  It  follows  that 
more  heat  would  be  needed  to  raise  50  g.  of  iron  1°  in  tempera- 
ture than  to  raise  50  g.  of  lead  1°. 

The  ratio  between  the  quantity  of  heat  required  to  raise  the 
temperature  of  a  certain  mass  of  any  substance  one  degree,  and 
the  quantity  of  heat  required  to  raise  the  same  mass  of  water 


1  French  engineers  also  use  a  calorie  1000  times  as  great ;  i.e.f 
1  kg.  of  water  is  the  basis  instead  of  1  g. 


282  HEAT 

one  degree,  is  the  specific  heat  of  that  substance;  or,  the  specific 
heat  of  a  substance  is  the  number  of  calories  required  to  change 
the  temperature  of  1  g.  of  that  substance  1°  C. 

TABLE  OF  SPECIFIC  HEAT 

Air  (conts.  pres.)   .  0.237  Aluminum .     .     .  0.214 

Water      .     .     .     .  1.000  Flint  glass .     .     .  0.117 

Ice 0.502  Iron       ....  0.113 

Steam      ....  0.480  Copper  ....  0.094 

Ether 0.516  Mercury     .     .     .  0.033 

Alcohol    ....  0.620  Lead      ....  0.031 

304.  The  Measurement  of  Specific  Heat.  —  A  convenient 
method  of  measuring  the  specific  heat  of  a  body  is  the  method 
of  mixtures.  This  depends  upon  the  fact  that  when  two 
bodies  that  are  at  different  temperatures  are  put  together, 
the  temperature  of  one  will  fall  and  that  of  the  other  will 
rise  until  they  have  reached  the  same  temperature.  It  also 
depends  upon  the  principle  that  the  heat  absorbed  by  the  cool 
body  in  heating  is  exactly  the  amount  given  out  by  the  hot  body 
in  cooling.  This  principle  is  fundamental  in  all  work  in 
specific  heat  and  may  be  stated  in  its  simplest  form  as  follows  : 
Heat  gained  =  Heat  lost.  The  quantity  of  heat  absorbed 
by  the  cool  body  in  heating  =  mass  X  change  in  temperature 
X  specific  heat.  The  quantity  of  heat  given  out  by  the  hot 
body  in  cooling  =  mass  X  change  in  temperature  X  specific 
heat.  That  is, 

Mis  =  M'W.  (50) 

EXAMPLE.  —  Two  pounds  of  fine  shot  at  90°  were  poured  into  one 
pound  of  water  at  15°,  and  the  resulting  temperature  was  20°. 
What  was  the  specific  heat  of  the  shot  ? 

From  Formula  50,  since  the  specific  heat  of  water  =  1, 
!X5Xl=2x70Xs, 

whence  s  =  ~  =  .036. 
140 


CALORIMETRY  283 

305.  Water  Equivalent.  —  It  is  evident  that  in  all  similar 
measurements,  account  should  be  taken  of  the  change  in 
temperature  of  the  containing  beaker,  or  calorimeter.     In 
order  to  do  this  it  is  necessary  to  find  its  water  equivalent,  or 
the  mass  of  water  that  will  require  the  same  number  of  calo- 
ries to  raise  its  temperature  one  degree  as  the  beaker  requires. 
Numerically  this  is  the  product  of  the  mass  of  the  beaker 
by  its  specific  heat. 

EXAMPLE.  • — Copper  shot  weighing  500  grams  at  a  temperature 
of  80°  C.  was  poured  into  a  20  g.  aluminum  beaker  containing 
300  g.  of  water  at  60°  C.  What  was  the  resulting  temperature? 

Water  equivalent  of  beaker  =  20  X  0.214  =  4.28.    Hence, 

(300  +  4.28)  (t  -  60)  X  1  =  500  (80  -  t)  (0.094) 
304.28 1  -  18,256.8  =  3760  -  47 1 
351.28  t  =  22,016.8 
t  =  62.7° 

306.  Heat  of  Fusion.  —  If  heat  is  applied  to  a  beaker  of 
crushed  ice,  it  will  be  noticed  that  while  the  ice  is  being 
melted  the  temperature  of  the  resulting  water  is  the  same 
as  that  of  the  ice,  i.e.,  zero.     The  effect  of  the  heat  is  not  to 
change  the  temperature,  but  to  change  the  physical  state 
from  solid  to  liquid. 

The  number  of  heat  units  required  to  melt  a  unit  mass 
of  a  substance  without  raising  its  temperature  is  called  the 
heat  of  fusion  of  the  substance.  On  solidification,  the  same 
amount  of  heat  is  given  out. 

Demonstration.  —  Pour  500  g.  of  water  at  80°  C.  into  a  glass 
beaker  weighing  100  g.,  and  into  this  put  150  g.  of  cracked  ice  as  dry 
as  possible.  Stir  the  ice  until  it  is  melted  and  take  the  resulting 
temperature  of  the  water.  It  will  be  found  to  be  about  43.8°  C. 
The  heat  of  fusion  of  ice  can  now  be  calculated  as  follows : 

The  heat  given  out  by  the  500  g.  of  water  and  by  the  100  g.  of 


284  HEAT 

glass  in  losing  36.2°  of  temperature  is  used  in  melting  the  ice  and 
raising  the  resulting  water  to  43.8°. 

Heat  given  out  by  the  water  =  500  X  36.2  X  1  =  18,100  calo- 
ries. 

Heat  given  out  by  the  beaker  =  100  X  36.2  X  .117  =424 
calories. 

Total  heat  given  out  =  18,524  calories. 

Heat  taken  up  by  ice  in  melting  =  150  X  heat  of  fusion  =  150  F 
calories. 

Heat  taken  up   by  resulting  water  =  150  X  43.8  X  1  =  6570 

calories. 

150  F   +  6570  =  18,524. 

150  F  =  11,954. 
F  =  79.7. 

The  heat  of  fusion  of  ice,  as  found  by  careful  experiments, 
is  80  calories.  This  means  that  it  takes  as  much  heat  to  melt 
one  gram  of  ice  as  it  would  to  raise  one  gram  of  water  from 
0°  to  80°. 

307.  Heat  of  Vaporization.  —  When  heat  is  applied  to  a 
beaker  of  water,  its  temperature  will  rise  until  the  boiling 
point  is  reached.     After  this  no  further  increase  in  the  tem- 
perature will  take  place,  however  rapid  the  boiling.     By 
continuing  the  experiment,  the  water  can  all  be  changed  into 
vapor.     The  number  of  heat  units  required  to  vaporize  a 
unit  mass  of  liquid  without  changing  its  temperature  is  its 
heat  of  vaporization.     When  the  vapor  changes  to  a  liquid, 
the  same  amount  of  heat  will  be  given  out.     Experiment  has 
shown  that  the  heat  of  vaporization  of  water  is  537  calories. 
This  means  that  the  heat  required  to  boil  away  1  g.  of  water 
is  5.37  times  as  much  as  is  required  to  raise  its  temperature 
from  zero  to  100°. 

308.  Curve  of  Heat  Effects.  —  An  effective  way  of  show- 
ing the  relation  between  the  heat  units  applied  and  the 


CALORIMETRY  285 

effects  produced  is  indicated  in  Fig.  257.  This  shows  graph- 
ically the  relation  between  the  heat  units  and  the  changes 
produced  when  heat  is  applied  to  1  g.  of  ice  at  —  18°  and  con- 
tinued until  the  latter  is  changed  into  steam  at  120°.  Hori- 
zontal distances  represent  calories  or  heat  units  (H.  U.), 
and  vertical  distances  represent  changes  of  temperature. 

Since  the  specific  heat  of  ice  is  0.502,  Mts  =  1  X  18  X 
0.502  =  about  9  calories  required  to  raise  the  ice  to  zero. 
80  calories  will  be  required  to  melt  it  ;  1  X  100  X  1  =  100 

Steam  at  120° 

, 


_ 
537  Hill.     steam  loo 


Zee  at  0° 

*'"-•"'•"&  1  fjf 

80  H.U.       Water  aT<)° 100  H. 

FIG.  257 

calories  to  raise  the  water  to  100° ;  537  calories  to  vaporize 
it ;  and,  since  the  specific  heat  of  steam  is  0.48,  Mts  =  1  X 
20  X  0.48  =  9.6  calories  to  raise  the  steam  to  120°.  The 
total  heat  applied  will  be  the  sum  of  these  amounts,  or 
735.6  calories. 

A  study  of  this  curve  will  be  of  great  assistance  in  making 
clear  the  relation  between  heat  units,  specific  heat,  heat  of 
fusion,  and  heat  of  vaporization,  and  will  help  in  the  solution 
of  problems  that  include  these  quantities. 

Questions 

1.  Suppose  you  were  making  a  number  of  determinations  in 
specific  heat,  would  there  be  any  advantage  in  using  the  same 
calorimeter  for  them  all? 
•  2.  What  do  t  and  t'  mean  in  the  equation  Mts  =  M't's'  ? 


286  HEAT 

3.  What  effect  does  the  high  specific  heat  of  water  have  upon 
the  rate  at  which  the  temperature  of  a  lake  will  be  changed? 

4.  If  the  temperature  of  a  room  is  —  4°  C.,  what  will  be  the  result 
of  bringing  pans  of  water  into  it  ? 

6.  Will  it  take  longer  to  melt  a  piece  of  ice  or  to  raise  the 
resulting  water  to  the  boiling  point,  if  the  heat  is  uniformly  applied  ? 

6.  What  do  horizontal  parts  of  the  curve  of  heat  effects,  Fig. 
257,  mean? 

Problems 

1.  How  many  calories  are  required  to  heat  200  g.  of  water  from 
15°  C.  to  the  boiling  point? 

2.  How  many  B.T.U.  are  required  to  heat  5  Ib.  of  water  from 
50°  F.  to  the  boiling  point? 

3.  A  piece  of  nickel  at  100°  C.  was  dropped  into  an  equal  weight 
of  water  at  0°  C.  and  the  resulting  temperature  was  9.8°  C.    Find 
the  specific  heat  of  the  nickel.  „ 

4.  What  is  the  water  equivalent  of  a  glass  beaker  weighing 
80  g.? 

5.  What  is  the  water  equivalent  of  a  copper  calorimeter  of  the 
same  weight? 

6.  What  is  the  water  equivalent  of  an  aluminum  calorimeter  of 
the  same  weight? 

7.  A  beaker  whose  water  equivalent  is  14  g  has  in  it  120  g.  of 
water  at  14°  C.    What  is  the  resulting  temperature  when  56  g.  of 
water  at  90°  C.  is  poured  into  it  ? 

8.  Into  the  same  beaker,  containing  50  g.  of  water  at  96°  C., 
200  g.  of  mercury  at  20°  C.  is  poured.     Find  the  resulting  tempera- 
ture. 

9.  An  aluminum  beaker  weighing  10  g.  contained  250  g.  of 
water  -at  12°  C.    What  was  the  resulting  temperature  when  250  g. 
of  water  at  92°  C.  was  poured  into  it? 

10.  What  mass  of  water  at  90°  C.  will  just  melt  2  kg.  of  ice  at  0°  ? 

11.  It  takes  10  minutes  to  melt  a  piece  of  ice.     How  long  will 
it  take  to  raise  the  resulting  water  to  the  boiling  point  over  the 
same  source  of  heat? 

12.  How  many  calories  will  it  take  to  melt  120  g.  of  ice  and  raise 
the  resulting  water  to  16°  C.? 


HEAT  AND  WORK  287 

13.  How  many  B.T.  U.  will  it  take  to  melt  6  Ib.  of  ice  and  raise 
the  resulting  water  to  48°  F.  ? 

14.  The  normal  temperature  of  the  body  is  98.4°  F.     How  many 
calories  are  required  to  raise  a  drink  of  300  g.  of  ice  water  to  that 
temperature? 

16.  It  takes  8  minutes  to  raise  the  temperature  of  a  certain 
quantity  of  water  from  the  freezing  to  the  boiling  point.  How  long 
will  it  take  to  boil  the  water  away  ? 

16.  How  much  steam  at  100°  C.  must  be  mixed  with  1  litre  of 
water  at  18°  C.  to  raise  Ks  temperature  to  90°  C.? 

17.  How  many  calories  would  be  required  to  melt  40  g.  of  ice  at 
zero,  raise  the  resulting  water  to  100°  C.,  and  vaporize  it? 

18.  How  many  grams  of  ice  would  be  required  to  change  the 
temperature  of  1200  g.  of  water  from  60°  F.  to  40°  F.  ? 

19.  A  cubic  foot  of  snow  melts  into  about  one  tenth  of  a  cubic  foot 
of  water.     How  many  B.T.U.  of  heat  would  be  required  to  melt 
the  snow  from  a  space  10  ft.  square  if  it  were  1  ft.  deep?    Could 
snow  be  removed  from  the  streets  economically  by  this  method? 

V.     HEAT  AND   WORK 

309.  General  Law.  —  We  have  seen  that  both  friction 
and  collision  give  rise  to  heat.     The  work  required  to  over- 
come the  friction  in  a  machine  is,  from  the  mechanical  stand- 
point, lost  work ;  in  reality  it  is  work  transformed  into  heat. 
The  relation  between  mechanical  work  and  heat  was  investi- 
gated  by  Joule,   who  established  the  following   principle : 
The  disappearance  of  a  certain  amount  of  mechanical  energy 
produces  an  equivalent  amount  of  heat.     The  converse  of  this 
law  is  equally  true :   The  disappearance  of  a  certain  amount 
of  heat  produces  an  equivalent  amount  of  mechanical  energy. 

310.  The  Mechanical  Equivalent  of  Heat.  —  The  number 
of  units  of  work  required  to  produce  one  heat  unit  is  called 
the    mechanical    equivalent    of    heat.     Joule's    experiments 
determined  that  the  number  of  foot  pounds  of  work  neces- 


288 


HEAT 


FIG.  258 


sary  to  heat  1  Ib.  of  water  1°  F.  is  772,  or  to  heat  1  Ib.  of  water 
1°  C.  is  1390.  This  is  called  Joule's  equivalent.  More  re- 
cent determinations  by 
Rowland  give  778  and 
1400  instead.  To  heat 
1  kg.  of  water  1°  C.  re- 
quires 427  kilogram- 
meters  of  work. 

Joule's  method  was 
as  follows :  A  cord  at- 
tached to  a  weight  was 
run  over  a  fixed  pulley 
and  wound  around  the 
axle  of  a  wheel,  with  paddles  at  the  other  end  of  the  axle. 
This  was  arranged  so  that,  on  letting  the  weight  fall,  the 
paddles  were  caused  to  rotate  in  a  known  quantity  of  water 
in  a  vessel.  The  weight  multiplied  by  the  distance  through 
which  it  falls  gives  the  mechanical  work,  and  the  mass  of 
water  multiplied  by 
the  change  of  tem- 
perature gives  the 
heat  units.  Joule's 
experiment  showed 
that  a  10-lb.  weight 
falling  through  77.2 
ft.  would  raise  the 
temperature  of  1  Ib. 
of  water  through  1°  F. 

FIG.  259 

311.  The  Pressure  of  Water  Vapor.  —  Demonstration.  — Place 
a  quantity  of  water  in  the  flask  A  (Fig.  259) .  Raise  the  water  to  the 
boiling  point,  and  after  it  has  boiled  a  short  time  remove  the  flame 


HEAT  AND  WORK 


289 


and  put  .in  a  rubber  stopper  with  tube,  as  shown  in  the  figure. 
Replace  the  flame,  and  the  steam  formed  by  boiling  will  collect  in 
the  flask  above  the  surface  of  the  water  and  increase  the  pressure. 
As  this  pressure  increases  it  will  do  work  by  forcing  water  out  of  the 
tube. 

In  the  process  of  evaporation  the  molecules,  moving 
in  every  direction,  strike  the  surface  of  the  liquid  from  below, 
and  some  of  them  escape  into  the  air.  If  the  temperature 
is  raised,  the  velocity  of  the  molecules  is  increased,  and  a 


0         10°     20°     30°     40°     50°     60°     70°     80°     90°    100°  110°    120°  130°  140' 
-     TEMPERATURE  IN  CENTIGRADE  DEGREES 

FIG.  260.  —  Pressure  of  Water  Vapor  at  Different  Temperatures 

greater  number  escape.  When  boiling  begins,  at  100°  under 
ordinary  atmospheric  pressure,  the  rise  of  temperature  is 
stopped,  and  all  the  heat  energy  applied  is  used  in  changing 
water  to  steam.  If  the  boiling  takes  place  in  a  closed  vessel, 
the  repeated  blows  of  the  molecules  of  the  vapor  upon  the 
surface  of  the  liquid  oppose  the  escaping  molecules  more 
and  more  as  the  vapor  increases  in  quantity  and  pressure ; 
and  if  the  temperature  is  kept  at  any  fixed  point,  as  100°, 

Rev. 


290 


HEAT 


the  boiling  soon  stops.  If  the  temperature  is  raised,  the 
molecular  velocity  increases,  the  internal  pressure  becomes 
greater  than  the  vapor  pressure,  and  boiling  recommences. 

312.  The  Steam  Engine.  —  A  steam  engine  is  a  machine 
for  transforming  the  pressure  and  expansive  power  of  steam 
into  mechanical  energy.  Since  the  steam  is  produced  by 
the  application  of  heat,  the  steam  engine  really  transforms 
heat  into  mechanical  energy.  So  great,  however,  are  the 
losses  in  the  burning  of  the  coal,  the  expansion  of  the 


FIG.  261. — Steam  Engine,  seen  from  above 

steam,  and  the  working  of  the  engine,  that  the  best  modern 
steam  engine  does  not  utilize  more  than  17  per  cent  of  the 
energy  in  the  coal. 

A  simple  form  of  steam  engine  is  shown,  partly  in  section, 
in  Figs.  261  and  262.  A  is  a  steam  pipe  connecting  a  boiler 
with  the  steam  chest  B.  The  live  steam  passes  from  the 
steam  chest  through  the  port  C  into  the  left  end  of  the  cylin- 
der, between  the  cylinder  head  D  and  the  piston  P.  The  pres- 
sure of  this  live  steam  forces  the  piston  to  the  right,  and  drives 
the  exhaust  steam,  on  the  other  side  of  the  piston,  out  of  the 
port  E  under  the  slide  valve  V,  and  out  of  the  exhaust  port  F, 
which  leads  either  to  a  condensing  chamber  or  to  the  open  air. 


HEAT  AND  WORK  291 

When  the  piston  has  been  forced  over  a  part  of  its  stroke, 
the  slide  valve  will  be  moved  by  its  rod  r  to  the  left,  closing 
C,  and  the  work  done  during  the  rest  of  the  stroke  will  be 
due  to  the  expansive  power  of  the  steam.  By  the  time  the 
piston  has  reached  the  end  of  its  stroke  to  the  right,  the 
slide  valve  will  be  moved  so  far  to  the  left  that  the  live  steam 
will  now  come  into  the  right  end  of  the  cylinder  through  E, 
and  the  exhaust  steam  in  the  left  end  will  go  out  of  the  ex- 


FIG.  262.  —  Steam  Engine,  seen  from  side 

haust  port  F,  through  the  port  C.  The  piston  rod  R  is  at- 
tached to  a  crank  arm  M  on  the  main  shaft  S,  and  in  this 
way  the  to-and-fro,  or  reciprocating,  motion  of  the  pis- 
ton is  changed  to  the  rotary  motion  of  the  shaft.  On 
the  shaft  are  fixed  one  or  two  heavy  flywheels  PF,,  the 
momentum  of  which  serves  to  give  steadiness  to  the  en- 
gine ;  and  one  or  more  belt  wheels,  over  which  run  the 
belts1  by  which  the  motion  of  the  shaft  is  transmitted,  to 
machinery. 

In  condensing  engines  the  exhaust  steam  passes  into  a 
compartment  containing  water  for  condensing  the  steam. 
The  condensation  greatly  reduces  the  back  pressure  which 
opposes  the  motion  of  the  piston.  In  noncondensing  en- 


292 


HEAT 


FIG.  263.  —The  Rocket 


gines,  such  as  the  locomotive,  the  exhaust  steam  passes  into 
the  open  air  —  sometimes  by  way  of  the  smokestack,  in  order 
to  increase  the  draught  through  the  fire  box.  The  back 
pressure  in  noncondensing  engines  is  the  pressure  of  the 
atmosphere. 

In  compound  engines,  the  steam 
gives  up  only  part  of  its  heat  and 
expansive  power  in  one  cylinder ; 
the  exhaust  steam  from  this  es- 
capes under  pressure  to  a  second 
cylinder,  where  it  does  more  work. 
By  thus  using  two  or  more  cylin- 
ders in  succession,  a  greater  per- 
centage of  the  energy  of  the  steam 
can  be  utilized.  A  comparison  of 

Stephenson's  locomotive,  the  Rocket,  built  in  1829  (Fig. 
263),  with  a  modern  type  of  locomotive  (Fig.  264),  shows 
the  development  that  has  taken  place. 

313.  The  Steam  Turbine  is  another  kind  of  steam  engine, 
in  which  expanding  steam  strikes  directly  upon  curved  blades 
in  a  wheel,  causing  it  to  rotate  by  impact  or  by  reaction,  just 
as  the  turbine  water  wheel  does  (§  147).  The  principle  of  a 
simple  turbine  is  illustrated  in  Fig.  265,  which  shows  how 
steam  is  delivered  to  the  blades  of  the  wheel  through  four 
tubes.  In  each  of  these  tubes  there  is  a  check  valve  which 
permits  only  the  proper  amount  of  steam  to  pass  through. 
On  escaping  through  this,  the  steam  acquires  a  high  velocity 
in  expanding,  and  strikes  upon  the  blades  of  the  wheel  with 
great  force. 

Another  type  of  turbine  is  divided  into  stages ;  that  is, 
there  are  several  rotating  wheels  for  each  set  of  steam  pipes. 


HEAT   AND   WORK 


293 


294 


HEAT 


Figure  266  shows  how  the  steam  may  be  passed  from  the 
steam  nozzles  N  through  three  sets  of  moving  blades  M  by 


FIG.  265.  — A  Simple  Steam  Turbine 

the  use  of  two  sets  of  stationary  blades  S.     By  this  arrange- 
ment the  energy  of  the  steam  is  used  with  a  high  degree 

of  efficiency.  The  steam  turbine 
is  used  to  drive  the  dynamos  in 
some  of  the  largest  plants  for  the 
generation  of  electric  current. 


M        M  A  jf 

FIG.  266 


314.  Gas  Engines. —  In  a  gas  en- 
gine the  motive  power  is  the  ex- 
pansion caused  by  the  explosion  of 
a  mixture  of  gas  and  air  in  a  cylin- 
der. The  expanding  gases  work 
against  a  moving  piston  as  the  ex- 
panding steam  dr>es  in  a  recipro- 


HEAT  AND   WORK 


295 


eating  steam  engine.     The  cycle  of  operations  in  a   four- 
stroke  or  four-cycle  engine  is  briefly  as  follows  (Fig.  267) : 


OUTLET 


-SPARK  PLUG. 


E 


FIG.  -67 

On  the  first,  outward,  stroke  of  the  piston  the  inlet  valve  is 
opened  and  a  mixture  of  gas  and  air  enters  the  cylinder 
through  the  inlet.  On  the  return  stroke  the  mixture  is 
compressed.  When  the  piston  begins  its  third  stroke,  which 

is  the  second  outward  stroke,  the 
gas  is  exploded  by  an  electric  spark 
and  expands,  and  on  the  fourth 
stroke  the  outlet  valve  is  opened 
and  the  products  of  the  combustion 
are  driven  from  the  cylinder  through 
the  outlet.  The  third  stroke  is 
the  only  one  from  which  power  is 
obtained. 

In  the  two-cycle  engine  the 
mixed  gases  enter  the  crank  case 
B  through  the  port  A,  Fig.  268, 
when  the  piston  C  is  at  the  top  of 
its  stroke  during  which  the  gas  in 
the  cylinder  D  is  compressed.  The 

spark  explodes  the  gas,  driving  the  piston  downward  and  com- 
pressing the  gas  in  the  crank  case.  The  gas  from  the  crank 


FIG.  268 


296  HEAT 

case  passes  through  the  transfer  port  as  shown  by  the  arrows, 
and  forces  the  exploded  gas  out  of  the  exhaust  port  E.  Both 
ports  are  closed  as  the  piston  begins  its  upward  motion  and 
the  rest  of  the  stroke  completes  the  compression. 

315.  The  Automobile.  —  The  gasoline  automobile  is  an 
excellent  example  of  a  self-contained  means  of  transportation. 
Its  essential  parts  are  the  chassis,  comprising  the 
frame  with  running  and  steering  gears;  the  motor,  an  in- 
ternal combustion  gasoline  engine;  the  transmission  system, 
by  means  of  which  the  energy  developed  in  the  engine  is 
applied  to  the  wheels  as  work;  the  ignition  and  lighting 
systems;  and  the  lubrication  and  cooling  systems. 

Since  the  frame  of  an  automobile  is  subjected  to  severe 
strains,  manufacturers  use  for  this  purpose  an  alloy  of 
steel  that  has  been  given  its  maximum  tensile  strength  by 
means  of  a  heat  treatment. 

The  engines  are  of  many  forms,  varying  in  the  number  of 
cylinders.  The  operation  of  the  piston  in  a  four-stroke 
engine  is  shown  in  Fig.  267.  The  gasoline  and  air  are  mixed 
in  proper  proportions  in  the  carburetor,  and  ignition  in  the 
cylinders  is  produced  by  electric  sparks. 

The  transmission  system  includes  the  speed-shifting 
gears  and  the  shafts  and  gears  required  for  changing  the 
reciprocating  movement  of  the  pistons  of  the  engine  into 
the  rotation  of  the  rear  wheels  of  the  chassis. 

Cooling  systems  are  of  various  kinds,  some  employing  a 
draft  of  air  forced  past  the  radiator,  others  a  forced  current 
of  water,  and  still  others  a  water  circulation  which  depends 
upon  the  difference  between  the  specific  gravity  of  cold 
and  of  hot  water. 

A  cross  section  of  the  engine,  transmission,  etc.,  of  a 
much-used  type  of  car  is  shown  in  detail  in  Fig.  269.  Figure 


HEAT   AND   WORK 


297 


|JU   1  111! 

ji  il  I  in 


£.3 
33 


Brake  Retracting 
Springs 

Pinion 

Spiral  Bean- 

Bevel  Drive 
Gear 


Driving  Pinion 
Adjusting  Nuts 


Differential 
Spiral  Spider 

Bevel  Driving  /  Wheel  Bearing 

Pinion       / 

Grease  Cups 


Oil  Filling 
Plug 


Differential  Gear 


FIG.  270.  —  Rear  Axle.  etc. 


Throttle  Lever 
Throttle  Lever  Stop  Screw 
Inlet  From  Tank 
Strainer 


Air  Horn 
Air  Shutter 
Automatic  Air  Weights 


Carburetor  Float 

Needle  Valve  Adjusting  Screw 


FIG.  271.  —  Carburetor 


HEAT  AND   WORK  299 

270  shows  details  of  the  mechanism  of  the  rear  axle 
and  its  accessories.  One  form  of  carburetor  is  shown  in 
Fig.  271. 

Questions 

1.  What  is  "  lost  work  "  in  a  machine? 

2*  What  is  meant  by  the  tefm  "mechanical  equivalent  of  heat "  ? 

3.  What  is  the  effect  of  raising  the  temperature  upon  the  expan- 
sive power  of  steam? 

4.  What  is  the  cause  of  the  sparks  that   fly  from  the  driving 
wheels  of  an  engine  when  the  brakes  are  put  on? 

5.  Which  is  greater  at   the  same  temperature,  the  pressure  of 
water  vapor,  or  the  pressure  of  ether  vapor?     Why? 

6.  Explain    why    water    boils  at  a   lower   temperature  under 
reduced  pressure. 

7.  Why  is  the  water  in  a  steam  boiler  at  a  higher  temperature 
than  100°  C.? 

8.  The  successful  use  of   automobiles   and   airplanes    depends 
upon  the  gasoline  engine.     Why? 

Problems 

1.  How  many  foot  pounds  of  work  must  be  done  on  5  Ib.  of 
water  to  raise  its  temperature  15°  C.? 

2.  56,000  foot  pounds  of  work  were  expended  on  4  Ib.  of  water. 
What  was  its  rise  of  temperature  in  Fahrenheit  degrees? 

3.  31, 120  foot  pounds  of  work  were  expended  in  raising  the  temper- 
ature of  a  certain  quantity  of  water  8°  C .   How  much  water  was  there ? 

4.  Suppose  the  500-lb.  head  of  a  pile  driver  falls  25  ft.,  and  that 
20  per  cent  of  the  kinetic  energy  on  striking  is  converted  into  heat. 
What  change  of  temperature,  in  Fahrenheit  degrees,  would  be  given 
to  1  Ib.  of  water  by  the  heat  generated? 

5.  Suppose  the  average  pressure  of  the  steam  that  is  used  in  an 
engine  is  60  Ib.  per  square  inch,  the  piston  head  is  10  in.  in  diameter, 
and  the  stroke  of  the  piston  is  18  in.     How  many  foot  pounds  of 
work  are  done  at  every  stroke  of  the  piston?     How  many  at  every 
rotation  of  the  flywheel?     How  many  per  minute  if  the  speed  is  106 
revolutions  per  minute?     What  is  the  horse  power  of  the  engine? 


CHAPTER  VIII 
MAGNETISM 

316.  Natural  Magnets.  —  Pieces  of  a  certain  kind  of  iron 
ore  have  the  property  of  attracting  iron ;  and  when  suspended 
so  as  to  swing  freely,  they  will  come  to  rest  in  a  nearly  north- 
and-south  direction.     They  are  called  natural  magnets.     The 
ore  is  called  magnetite,  from  Magnesia  in  Asia  Minor  near 
which  it  was  first  found. 

317.  Artificial  Magnets.  —  Demonstration.  —  Select  a  sewing 
needle  that  has  no  attraction  for  iron.     Rub  it  gently  from  the 
middle  toward  the  point  across  one  end  of  a  natural  magnet  (a 
bar  magnet  will  serve  as  well) ;   then  rub  the  other  half  across  the 
other  end  of  the  magnet.     Hold  one  end  of  the  needle  near  some  iron 
filings.     They  will  be  found  to  cling  to  the  needle. 

A  piece  of  iron  or  steel  that  has  the  property  of  attracting 
iron  as  in  the  above  demonstration  is  called  an  artificial 
magnet.  This  name  is  not  very  appropriate,  and  is  used 
simply  to  distinguish  magnets  composed  of  manufactured 
iron  or  steel  from  natural  magnets. 

Artificial  magnets  are  made  in  various  forms.  A  bar 
magnet  is  a  straight  bar ;  a  horseshoe  magnet  is  a  bar  bent 
into  U  shape. 

318.  Permanent  and  Temporary  Magnets. — Demonstration. 

— Repeat  the  above  demonstration,  using  a  bar  of  soft  iron  instead 
of  the  steel  needle.  Does  the  bar  become  a  magnet?  Now  hold 
one  end  of  a  soft  iron  bar  on  or  near  the  end  of  a  magnet,  and  bring 
the  other  end  of  the  bar  near  some  iron  filings.  What  is  the  result  ? 

300 


MAGNETISM 


301 


Pieces  of  soft  iron  can  be  made  to  act  as  temporary  magnets 
while  near  another  magnet,  but  they  retain  hardly  any 
magnetism  after  the  other  magnet  is  removed.  Pieces  of 
steel  retain  their  magnetism  to  a  great  degree  and  hence 
can  be  made  into  permanent  magnets. 

3,19.  Magnetic  and  Nonmagnetic  Substances. — Demonstra- 
tion. —  Place  on  a  table  a  collection  of  a  dozen  different  materials, 
nails,  screws,  pins,  coins,  pencils,  wire,  paper,  etc.,  —  and  try  to 
pick  them  up  with  &  magnet.  Part  of  them  will  be  picked  up,  but 
upon  others  the  magnet  will  have  no  effect  whatever. 

Those  substances  that  are  attracted  by  a  magnet  are  called 
magnetic  substances,  while  those  that  are  not  attracted  by 
it  are  called  nonmagnetic  substances.  Iron  and  steel  are 
magnetic;  also,  to  a  less  degree,  nickel  and  cobalt.  Some 
ores  of  iron  are  magnetic,  while  others  are  not.  Nonmag- 
netic iron  ores  can  be  made  magnetic  by  being  strongly 
heated,  as  in  the  flame  of  a  blowpipe. 

320.  Polarity.  —  Demonstrations. — Lay  a  bar  magnet  upon  a 
table  covered  with  small  nails,  and  then  lift  it  by  the  middle.  It  will 
be  found  that  the  nails 
cling  to  the  magnet,  the 
greater  number  being 
near  the  ends,  as  in  Fig. 
272.  The  two  points 
near  the  ends  where  the 
most  nails  cling  indicate 
the  position  of  the  poles 
of  the  magnet. 

Suspend  the  ba'r 
magnet  by  a  thread  at- 
tached to  its  middle  point,  and  after  swinging  back  and  forth  for 
a  time  it  will  finally  coine  to  rest  in  a  direction  that  is  nearly  north 
and  south, 


FIG.  272 


302 


MAGNETISM 


It  has  been  agreed  to  call  the  end  which  points  to  the 
magnetic  north  the  +  or  north  pole  and  the  other  the  —  or 
south  pole.  The  strictly  correct  names  would  be  north-seek- 
ing pole  and  south-seeking  pole.  A  body  with  such  poles 
is  said  to  be  polarized,  and  to  possess  polarity. 

321.  The  Magnetic  Needle  is  a  small  bar 
magnet  suspended  by  a  thread  or  balanced 
upon  a  pivot  (Fig.  273).  It  is  used  in  many 
instruments,  as  in  the  compass.  If  we  should 
continuously  follow  the  direction  in  which  it  points,  our 
path  would  be  a  magnetic  meridian ;  and  that  spot  in  the 
Arctic  regions  where 
all  magnetic  merid- 
ians meet  is  called  the 
north  magnetic  pole. 

Demonstrations.  — 

Magnetize   a    sewing 

needle   by    drawing    it 

across    the  ends  of    a 

bar  magnet.    Begin  the 

stroke  at  the  middle  of 

the  needle  and  end  it 

at  the  point,  drawing 

it  across  the  +  end  of 

the  magnet.      Do  this 

ten    or    twelve    times. 

Reverse  the.  needle  and 

draw  it  across  the  — 

end  of  the  magnet,  be-  FJG.  274.  —  Magnetic  Meridians 

ginning  at  the  middle 

of  the  needle  and  ending  at  the  eye.     Unravel  a  fine  silk  thread, 

and  tie  a  single  strand  around  the  middle  of  the  needle.     When  you 

have  balanced  the  needle  so  that  it  will  hang  horizontally,  fasten 


MAGNETISM 


303 


the  thread  in  place  by  a  bit  of  beeswax  or  sealing  wax,  and  you 
have  a  magnetic  needle  that  will  serve  for  many  experiments. 

Suspend  the  needle  and  find  the  magnetic  meridian.  Observe 
which  end  of  the  needle  points  north,  and  notice  whether  or  not  it  is 
the  end  that  was  drawn  over  the  north  end  of  the  magnet. 

Make  a  small  bar  magnet  out  of  a  good-sized  knitting  needle.  In 
stroking  it  with  the  magnet,  lay  it  upon  a  piece  of  board  and  stroke 
it  with  the  +  end  from  the  middle  to  one  end  of  the  needle.  Re- 
verse the  needle  and  magnet  and  repeat.  In  order  to  make  a 
strong  magnet,  the  steel  + 

must  be  stroked  a  great         + 
many  times.  Test  it  with 
iron  filings  and  nails. 


FIG.  275 


FIG.  275  a 


322.  Mutual  Ac- 
tion of  Magnets.  — 
Demonstration.  —  Bring 
the  +  end  of  a  bar  magnet  near  the  +  end  of  a  magnetic  needle  and 
note  the  result.  Bring  the  —  end  of  the  magnet  near  the  +  end  of 
the  needle  and  observe.  Make  the  same  experiment  on  the  —  end 
of  the  needle. 

The  results  of  the  above  demonstration  may  be  stated 
in  the  following  terms :  Like  poles  repel  and  unlike  poles 
attract  each  other.  This  law  is  a  fundamental  one  in  mag- 
netism and  should  be 
made  very  familiar. 
The  force  of  the  repul- 
sion or  the  attraction 
varies  directly  as  the 
magnetic  strength  of 
the  poles  and  inversely 
as  the  square  of  the 
distancebetween  them. 


FIG.  276 


Demonstrations.  —  Lay  a  horseshoe  magnet  upon  a  table.     Pass 
a  light  thread  through  the  eye  of  a  magnetized  sewing  needle,  and 


304 


MAGNETISM 


by  careful  manipulation  it  can  be  brought  to  remain  in  a  horizontal 

position  over  the  ends  of  the  magnet,  as  in  Fig.  276,  although  only 

slightly  supported  at  one  end.     Ex- 
plain. 

Magnetize  a  number  of  sewing 
needles  so  that  their  eyes  will  be 
south  poles  and  their  points  north. 
Thrust  them  through  small  corks, 
leaving  the  eye  half  an  inch  above. 
Float  three  of  them  in  a  glass  of 
water.  Notice  their  positions,  and 
explain.  Now  bring  the  south  pole 
of  a  bar  magnet  vertically  down 
over  the  middle  of  the  glass.  Ex- 
plain the  result.  Reverse  the  magnet 
and  repeat.  Explain.  Increase  the 

number  of  needles  and  repeat.     These  are  called  Mayer's  floating 

magnets. 

323.  The  Distribution  of  Magnetism  in  a  Magnet  may  be 
found  by  laying  a  bar  magnet  upon  a  table,  suspending  above 
it  a  magnetized  sewing  needle,  and  passing  the  needle  from 
end  to  end.     At  the  middle  of  the  magnet  th'e  needle  will  be 
parallel  to  it.     This 

is  called  the  neutral 
point,  which  may  be 
defined  as  that  point 
in  a  magnet  where 
all  the  lines  of  force 
are  within  the  mag- 
net, none  of  them  passing  into  the  air.  At  other  points  the 
needle  will  dip  more  or  less,  as  in  Fig.  278.  At  two  points 
near  the  ends  the  needle  stands  practically  vertical ;  these 
points  locate  the  poles. 

324.  Lines  of  Force.  —  A  north  magnetic  pole  placed  near 


FIG.  278 


MAGNETISM 


305 


the  +  end  of  a  bar  magnet  is  at  the  same  time  repelled  by 
the  H-  end  and  attracted  by  the  —  end,  and  each  force  varies 
inversely  as  the  square  of  the  distance.  Consequently,  if 
the  pole  were  free  to  move  under  the  sole  influence  of  the  bar 
magnet,  it  would  follow  a  curved  path  called  a  line  of  magnetic 
force,  and  would  come  to  rest  in  contact  with  the  —  end  of 
the  magnet.  By  starting  the  pole  at  different  points,  an  in- 
finite number  of  such  lines  of  force  could  be  described.  The 
direction  of  a  line  of  force 
means  the  direction  in 
which  a  free  north  pole 
would  move.  Though  a 
free  north  pole  cannot 
exist  (there  is  no  north 
pole  without  its  accom- 
panying south  pole),  this 
direction  at  any  point 
will  be  that  along  which 
the  north  pole  of  a  short 
piece  of  magnetized 
needle  suspended  by  a 
thread  will  tend  to  move. 


i 


* 


\ 


FJG.  279.  —  Lines  of  Force 

This  needle  will  turn  so  as  to 
lie  as  nearly  as  possible  in  the  line  of  force,  because  in  any 
other  position  the  forces  acting  on  the  two  poles  of  the  needle, 
not  being  in  line  with  the  needle,  would  form  a  couple  and 
cause  rotation.  A  few  lines  of  force  are  shown  in  Fig.  279, 
some  complete  and  some  in  part. 

Demonstration.  —  Lay  a  bar  magnet  upon  the  table  and  cover 
it  with  a  sheet  of  white  paper.  Put  over  this  a  thin  glass  plate  and 
sift  iron  filings  evenly  over  it.  The  sieve  for  this  purpose  can  be 
made  by  melting  the  solder  that  holds  on  the  bottom  of  a  tin  can, 
removing  the  bottom,  and  tying  over  the  can,  in  its  place,  a  piece  of 

Rev. 


306  MAGNETISM 

thin  muslin  or  cheesecloth.  Rap  the  plate  gently  with  a  lead  pencil ; 
the  filings  will  move  at  every  blow,  and  will  arrange  themselves  in 
lines  that  show  clearly  the  paths  of  the  lines  of  force. 

Suspend  a  half-inch  piece  of  magnetized  sewing  needle  quite  near 
the  plate  used  in  the  above  demonstration.  Notice  that  it  places 
itself  in  line  with  the  filings. 

325.  A  Permanent  Record  of  Lines  of  Force  may  be  made 
by  repeating  the  above  demonstration  in  a  dark  room  with 
a  ruby  lantern  for  light,  and  using  an  ordinary  photographic 
dry  plate  for  the  glass  plate.     The  dry  plate  is  placed  upon 
the  magnet,  film  side  up,  the  filings  are  sifted  upon  it,  and  the 
plate  is  rapped  until  the  position  of  the  lines  of  force  is  clearly 
brought  out.     The  exposure  is  made  by  burning  a  match 
about  a  foot  above  the  plate.     On  developing  the  plate  in 
the  usual  way  a  negative  is  obtained  from  which  may  be  made 
prints  showing  the  lines  formed  by  the  filings. 

326.  Magnetic  Permeability.  —  Demonstration. — Repeat  the 
demonstration  in  §  324,  after  laying  a  soft  iron  bar  beside  the  magnet. 
What  effect  does  this  have  on  the  lines  of  force  ? 

Lines  of  force  pass  through  air  and  other  nonmagnetic 
substances  with  greater  difficulty  than  through  iron.  When 
a  piece  of  iron  is  introduced  into  a  space  where  there  are 
lines  of  magnetic  force,  it  offers  a  path  of  less  resistance, 
and  causes  a  distortion  of  the  lines  of  force  from  their  previous 
distributions.  The  iron,  offering  a  smaller  resistance  to  the 
passage  of  the  lines  of  force  than  the  air,  is  said  to  have  a 
y  s  greater  permeability.  For 

this  reason  a  watch  in  a 


8  thin   iron    case  does   not 

become  magnetized. 

Demonstration.  —  Suspend  a  nail  from  near  one  end  of  a  bar 
magnet,  as  in  Fig.  280.    Slide  a  second  magnet  of  equal  strength 


MAGNETISM 


307 


over  it  and  observe  results.     Reverse  the  second  magnet,  and  again 
slide  it  over  the  first.     Explain  both  results. 

327.  Action  of  Lines  of  Force.  —  The  conception  of  lines 
of  force  is  that  they  form  dosed  circuits  (being  continued 
through  the  substance  of  a  magnet  as  in  Fig.  279),  take  the 
path  of  least  resistance,  tend  to  shorten  like  stretched  rubber  bands, 
and  when  going  in  the  same  direction  mutually  repel  each  other. 


FIG.  281 

P ":'-  - 

• 

The  repulsion  between  lines  of  force  going  in  the  same 
direction  is  illustrated  in  Fig.  281,  which  shows  the  lines 
formed,  by  the  method  of  §  325,  on  a  plate  laid  over  a  horse- 
shoe and  a  bar  magnet.  Notice  that  the  lines  of  filings, 
which  indicate  the  paths  of  these  lines  of  force,  lie  side  by 
side  and  run  off  parallel  to  each  other  to  the  right  of  the  two 
north  poles,  but  that  they  run  from  both  north  poles  to  the 
south  pole  in  paths  that  are  either  straight  or  curved,  de- 
pending upon  their  position.  The  mutual  side  push  of  lines 


308  MAGNETISM 

of  magnetic  force  that  pass  through  the  air  in  the  same 
direction,  and  also  the  fact  that  all  lines  of  magnetic  force 
are  closed  circuits  under  tension  like  elastic  bands,  will  be 
found  of  especial  importance  in  connection  with  electric 
currents. 

328.  Magnetic  Field ;  Measurements.  —  A  magnetic  field 
is  a  space  in  which  there  are  lines  of  magnetic  force.     The 
field  usually  considered  is  some  limited  area,  always  perpen- 
dicular to  the  lines  of  force. 

If  the  like  poles  of  two  magnets  of  equal  strength,  when 
one  centimeter  apart,  repel  each  other  with  a  force  of  one 
dyne,  each  is  called  a  unit  pole.  A  magnetic  field  of  unit 
strength  is  one  where  a  unit  pole  would  be  acted  upon  with 
a  force  of  one  dyne.  One  line  of  force  is  called  a  maxwell. 
A  magnetic  field  of  unit  intensity,  that  is,  one  having  one 
line  of  force  per  square  centimeter,  is  called  a  gauss. 

A  small  bar  of  hardened  steel  will  retain  about  800  lines  of  force 
per  square  centimeter;  that  is,  the  intensity  of  its  field  is  800 
gausses,  and  if  the  bar  is  2  cm.  wide  and  1  cm.  thick,  there  are  1600 
maxwells  in  the  field  adjacent  to  the  end  of  the  magnet. 

329.  The  Magnetic  Condition  of  the  Earth.  —  We  have 
seen  that  the  +  pole  of  a  magnet  repels  the  +  pole  of  a 
needle  and  attracts  the  --  pole.     We  have  also  seen  that 
the  needle  tends  to  set  itself  in  the  direction  of  the  lines  of 
force,  and  that  a  magnetic  needle,  suspended  so  as  to  swing 
freely,  points  with  its  north  end  toward  the  magnetic  north. 
It  is  evident,  then,  that  the  earth  acts  as  a  great  magnet,  and 
that  the  pole  toward  which  the  north-seeking  end  of  the 
needle  points  has  the  same  kind  of  polarity  as  the   —   or 
south  end  of  a  bar  magnet.    The  fact  that  the  north  magnetic 
pole  of  the  earth  and  the  north  pole  of  a  magnetic  needle 


MAGNETISM 


309 


FIG.  282 


are  of  unlike  signs  has  given  rise  to  some  difficulty  in  giving 
them  names  that  are  scientifically  correct;  but  the  name 
north  for  the  +  pole  of  the  needle  is  generally  adopted. 

330.  Inclination  or  Dip.  —  In  Fig.  278  we  see  that  in  every 
position  but  one  the  needle  dips  toward  one  of  the  poles. 
In  a  similar  way  a  needle  that  has  been  ^-- 

balanced  horizontally  on  a  pivot,  and 
then  magnetized,  will  not  remain  hori- 
zontal, but  will  dip  toward  the  nearer 
pole  of  the  earth.  The  angle  of  dip,  that 
is,  the  angle  the  needle  makes  with  a 
horizontal  line,  increases  as  the  distance 
from  the  magnetic  equator  increases.  At  the  magnetic 
equator  there  is  no  dip,  while  at  the  magnetic  poles  the 

needle  will  place  itself 
in  a  vertical  direction. 

The  true  pole  is  be- 
neath the  surface.  The 
needle,  except  at  the  ap- 
parent pole  itself,  does 
not  point  directly  to- 
ward the  true  pole,  but 
instead  lies  tangent  to 
a  curved  line  of  force, 
such  as  one  of  those 
shown  in  Fig.  282. 

331.  The    Dipping 

Needle.— Figure  283 
shows  a  form  of  needle 
that  is  used  to  deter- 
mine  the  dip.  It 
j?IGt  283  consists  of  a  magnetic 


310  MAGNETISM 

needle  swinging  on  a  horizontal  axis  which  is  in  a  direction 
perpendicular  to  the  magnetic  meridian.     The  needle  itself 
swings  in  a  vertical  plane  in  the  magnetic  meridian.     It  is  so 
balanced  that  it  will  come  to  •  rest 
in  a  horizontal  position  before  being 
magnetized.     After  it  is  magnetized 
and   placed    in   the   magnetic    meri- 
dian it  will  set  itself  in  the  line   of 
dip.* 

The  juiner's  dipping  needle,  Fig. 
284,  is  a  portable  instrument  of  the 
FIG.  284  same  general  type,  that  is  u&ed  to 

detect  the  presence  of  magnetic  ores. 

332.  Magnetic  Declination.  —  At  most  places  the  mag- 
netic needle  does  not  point  to  the  true  north,  but  instead  a 
little  to  the  east  or  west  of  north.     The  chief  reason  for  this 
is  that  the  north  pole  of  the  earth  and  the  magnetic  north 
pole  do  not  coincide.     The  magnetic  north  pole  is  about 
latitude  70°  N.  and  longitude  96°  W. 

By  reference  to  Fig.  285,  it  is  readily  seen  that  in  the 
Eastern  states,  as  in  Maine,  for  example,  the  needle  points 
to  the  west  of  the  true  north,  while  in  California  it  points 
to  the  east  of  the  true  north.  The  angle  between  the  direc- 
tion of  the  needle  at  any  place  and  the  true  meridian  at  that 
place  is  the  declination.  In  some  places  the  needle  points 
to  the  true  north ;  a  line  drawn  through  such  places  is  called 
an  agonic  line  or  line  of  no  declination.  Figure  285  shows 
not  only  the  agonic  line  in  the  United  States,  but  also  a  line 
drawn  through  places  where  the  declination  is  1°  west, 
another  where  the  declination  is  1°  east,  and  so  on. 

333.  Variation.  —  The  angle  of  declination  at'  any  place 
changes  from  year  to  year  by  an  amount  which  is  not  uni- 


MAGNETISM 


311 


FIG.  285.  —  Lines  of  Equal  Magnetic  Declination 

form,  and  which  is  called  the  annual  variation.  In  surveying 
land  it  is  very  important  that  the  amount  of  this  variation 
should  be  known,  and  records  of  this  change  are  made  and 
preserved.  By  comparing  these  records,  it  is  seen  that  the 
agonic  line  is  moving  westward,  i.e.,  the  declination  of  places 
east  of  the  line  is  increasing,  and  that  of  places  west  of  the 
line  is  diminishing.  The  annual  change  at  Philadelphia 
is  about  4  minutes. 

334.  Magnetic  Survey  of  the  Ocean.  —  Since  the  course 
of  a  ship  at  sea  is  mainly  dependent  upon  the  readings  of  the 
compass  needle,  it  is  of  especial  importance  that  the  magnetic 
dip,  declination,  and  variation  over  the  surface  of  the  oceans 
should  be  accurately  known.  For  the  purpose  of  determin- 
ing these  values  experimentally,  the  Department  of  Terres- 
trial Magnetism  of  the  Carnegie  Institution  at  Washington, 
D.  C.,  built,  in  1909,  a  remarkable  sailing  ship,  the  Carnegie. 

Almost  no  iron  or  other  magnetic  material  was  used  in  this 
ship  and  the  little  that  was  used  was  placed  so  far  from  the 


FIG.  286.  —  The  Non-Magnetic  Ship  Carnegie 


FIG.   287 


FIG.  2bS 


312 


MAGNETISM  313 

magnetic  instruments  that  it  had  no  disturbing  effect  upon 
them.  Even  the  auxiliary  gasoline  engine  is  almost  entirely 
of  bronze.  Because  of  this  non-magnetic  construction  the 
Carnegie  has  been  able  to  correct  errors  of  from  one  to 
fifteen  degrees  in  the  magnetic  charts  used  by  mariners. 

In  five  cruises  nearly  200,000  nautical  miles  were  covered, 
observations  being  taken  every  100  or  150  miles.  In  October, 
1919,  the  Carnegie  started  on  her  sixth  voyage  to  extend 
over  a  period  of. more  than  two  years,  gathering  data  for  the 
correction  of  magnetic  variation  charts. 

Figure  287  shows  the  method  of  making  observations ;  the 
most  delicate  instruments  are  permanently  mounted  and 
placed  inside  the  dome.  At  the  left  of  the  dome  is  a  gimbal 
stand,  shown  on  a  larger  scale,  with  a  sea  dip  circle  mounted 
upon  it,  in  Fig.  288. 

335.  Magnetic  Induction.  —  We  have  seen  that  when  a 
piece  of  soft  iron  is  put  in  contact  with  a  bar  magnet,  it 
becomes  a  magnet  itself  and  will  attract  iron.  When  a 
magnet  is  dipped  in  iron  filings  or  nails  and  lifts  a  number 
of  them  attached  to  one  another,  it  is  because  each,  has 
become  a  distinct  magnet.  This  influence  of  a  magnet 
over  pieces  of  iron  or  steel,  by  which  they  are  made  magnets, 
is  called  magnetic  induction,  and  extends  to  a  considerable 
distance  from  the  magnet. 


nniiiiiiiiiiiiiiiminf iiiiiiiiiiiiiiiiHiiiiiiiiiiiiiniiiiiiiiimiiiniiiiiiiiiiiiiiiiii iiiiiiitiuiiiiimiiiiiiiiiii t 

FIG.  289 


Demonstration.  —  Place  a  bar  magnet  upon  a  table,  and  at  one 
end,  in  line  with  it  and  about  an  inch  away,  put  a  large  nail,  as  in 
Fig.  289.  Bring  smaller  nails  near  the  end  of  the  large  one,  and 
observe  that  it  attracts  them.  Test  the  end  of  the  nail  with  the 
magnetized  sewing  needle,  to  find  which  kind  of  polarity  it  has. 


314  MAGNETISM 

This  property  possessed  by  a  magnet  —  of  inducing  polar- 
ity in  magnetic  substances  that  are  near  it  —  is  the  basis  of  a 

great  many  magnetic 
phenomena.    By  the 
J  application    of    this 
principle,    and    that 
~|  of  the  mutual  action 
we  see 


FIG.  290 

why  a  magnet  at- 
tracts ordinary  pieces  of  iron  —  an  iron  ball,  for  instance. 
Suppose  the  ball  to  be  at  a  distance  from  the  magnet,  as 
in  (a),  Fig.  290.  The  ball  is  practically  beyond  the  influ- 
ence of  the  magnet  and  remains  in  a  neutral  condition. 
When,  however,  it  is  brought  near  the  magnet,  as  in  (b), 
induction  takes  place,  and  the  ball  becomes  polarized,  the 
side  nearest  the  magnet  being  S  and  the  other  side  N.  Now 
between  the  N  of  the  magnet  and  the  S  of  the  ball  there  is 
attraction,  while  between  the  N  of  the  magnet  and  the  N 
of  the  ball  there  is  repulsion;  but  as  the  S  of  the  ball  is 
much  nearer  the  N  of  the  magnet  than  the  N  of  the  ball  is, 
the  attraction  is  much  greater  than  the  repulsion. 

We  see  also  why  the  iron  filings  in  §  324  indicate  the  lines  of 
force.  Each  particle  of  iron  becomes  a  magnet  by  induction,  and, 
like  the  magnetized  needle,  turns  so  that  its  two  poles  are  in  a  line 
of  force.  Its  poles  also  are  attracted  by  the  adjacent  unlike  poles 
of  other  particles,  and  thus  the  particles  cling  together,  with  their  -j- 
poles  turned  toward  the  —  end  of  the  magnet,  in  lines  of  force. 

336.  The  Inductive  Action  of  the  Earth  can  be  shown 
most  strikingly  as  follows : 

Demonstration.  —  Select  a  soft  iron  bar  about  an  inch  in  diame- 
ter and  three  or  four  feet  long.  Holding  it  horizontally  in  an  east 
and  west  line,  present  its  ends  successively  to  the  N  and  S  ends  of 


MAGNETISM 


315 


a  magnetic  needle.  Both  ends  will  attract  each  end  of  the  needle, 
showing  that  the  bar  is  not  polarized.  Next  hold  it  in  the  line  of 
dip,  with  the  lower  end  at  the  side  of  the  needle  and  near  the  north 
end.  The  needle  will  be  repelled  at  once,  showing  that  in  this  posi- 
tion the  bar  is  polarized.  Reverse  the 
bar  and  make  the  same  test  with  the 
needle,  and  the  needle  will  show  that  the 
polarity  of  the  bar  is  reversed.  Bring 
the  bar  into  the  first  horizontal  posi- 
tion and  again  it  will  attract  both  ends 
of  the  needle,  showing  that  it  is  not 
polarized.  Place  the  bar  again  in  the 
line  of  dip  and  give  it  one  or  two  sharp 
blows  with  a  hammer.  Now  place  it 
in  the  first  horizontal  position ;  and  on 
testing  it  with  the  needle  it  is  found  to 
be  polarized.  Hold  it  horizontally  in 
an  east  and  west  line  and  give  it  a  few  ..... 
sharp  blows;  and  it  will  be  found  to 
be  not  polarized. 

With  the  magnetized  sewing  needle,  test  the  steel  or  iron  rods 
about  the  building  for  polarity.  Most  of  them  will  be  found  polar- 
ized, especially  if  they  have  been  in  a  vertical  position.  What  is 
the  polarity  of  the  lower  end  of  a  vertical  rod?  Why? 

337.  Molecular  Magnets.  —  If  we  consider  the  molecules 
of  iron  to  be  polarized,  we  can  explain  magnetism  and  mag- 
netic induction  as  follows.  A  magnet  is  a  piece  of  iron  com- 
posed of  molecular  magnets  which  lie  partly  or  wholly  in  a 
uniform  direction.  When  a  piece  of  iron  is  in  a  neutral 
condition,  not  polarized,  the  molecular  magnets  of  which  it 
is  composed  have  no  uniform  direction,  their  positions  being 
determined  by  the  mutual  action  they  have  upon  one  another. 
When,  however,  a  magnet  is  brought  near,  their  mutual  ac- 
tion is  overpowered  by  the  greater  force  of  the  magnet,  they 
assume  parallel  directions,  and  the  iron  becomes  a  magnet. 


FIG.  291 


MAGNETISM 

338.  The  Effect  of  Breaking  a  Magnet. — Demonstration.  — 

Magnetize  a  knitting  needle.  Determine  its  poles.  File  a  notch  at 
the  middle  and  break  it.  Examine  for  polarity  again,  and  compare 
with  the  polarity  the  needle  had  before  breaking.  Break  one  of 
these  pieces  in  the  middle  and  examine  for  polarity.  On  a  drawing 
of  the  broken  needle,  mark  the  polarity  of  each  end  of  each  piece. 

339.  The  Effect  of  Heating  a  Magnet.  —  If  a  sewing  needle 
is  magnetized  and  then  heated  to  redness  by  being  held  in 
the  flame  of  a  Bunsen  burner,  it  will  be  found,  on  testing 
it  after  cooling,  that  it  has  lost  practically  all  its  magnetism. 
This  is  probably  due  to  the  fact  that,  in  heating,  the  vibra- 
tions of  the  molecules  have  increased  in  velocity  until  they 
no  longer  retain  the  positions  which  determine  the  polarity 
of  the  magnet.     If  the  needle  is  heated  red-hot  from  end  to 
end,  it  cannot  be  picked  up  by  a  magnet,  which  shows  that  at 
that  temperature  steel  is  not  a  magnetic  substance. 

Questions 

1.  How  do  natural  magnets  become  polarized? 

2.  Suppose   a   magnetic  needle  is  attracted  by  a  certain  body; 
does  this  prove  that  the  body  is  a  magnetic  substance?     Does  it 
prove  that  the  body  is  polarized?      What  is  the  only  action  that 
proves  polarity? 

3. .  In  what  direction  would  the  north  end  of  a  magnetic  needle 
point  at  the  northern  end  of  Greenland? 

4.   What  is  meant    by  a  uniform    magnetic  field?     Give  an 
example. 

5.  The  square  piece  of  land  shown  in  Fig. 
292  was  surveyed,  starting  from  the  point  A. 
The  line  AB  was  found  to  have  the  direction 
N.  20°  E.  An  old  survey  gave  the  direction  of 
this  line  as  N.  16°  E.  Show  by  a  drawing  the 
effect  of  running  this  out  on  the  old  direc- 
tions, without  allowing  for  a  change  in  the 
Fi«.  292  declination. 


MAGNETISM  317 

6.  Why  are  scissors,  knives,  and  other  steel  tools  often  found  to 
be  magnets? 

7.  What  position  would  a  magnetic  needle  take  if  suspended,  at* 
the  earth's  surface,  over  the  magnetic  north  pole?     Over  the  mag- 
netic south  pole?     At  the  magnetic  equator? 

8.  Suppose  you  were  to  place  a  magnetic  needle  upon  a  thin  cork 
disk  on  the  surface  of  water  in  a  wooden  pail.     Would  it  go  toward 
the  north?    Explain.     Make  the  experiment. 

9.  What  is  the  effect  of  near-by  iron  ore,  iron  posts,  steel  wire 
fences,  and  the  like,  upon  the  surveyor's  compass? 

10.  Why  are  the  iron  posts  of  a  fence  generally  found  to  be  mag- 
netized?    What  is  the  polarity  of  their  upper  ends? 

11.  Show  by  a  drawing  the  polarity  of  a  magnet  broken  in  two. 

12.  A  test  tube  filled  with  iron  filings  can  be  magnetized  by 
stroking  with  a  bar  magnet.     Explain. 

Problems 

1.  A  bar  magnet  sends  out  500  lines  of  force.     How  many 
dynes  of  attraction  will  there  be  between  the  +  pole  of  this  magnet 
and  the   —  pole  of  a  magnet  of  equal  strength  if  they  are  5  cm. 
apart? 

2.  It  requires  a  pull  of  12,000  dynes  to  keep  the  +  pole  of  a 
magnet,  having  a  strength  of  200  lines  of  force,  from  going  toward 
the  pole  of  another  magnet  placed  2  cm.  from  the  first.     What  was 
the  polarity  of  the  second  magnet  and  what  was  its  strength? 

3.  If  two  bar  magnets  placed  end  to  end  are  repelled  with  a 
force  of  1200  dynes  when  the  poles  are  20  cm.,  apart,  what  will  be 
the  repulsion  when  they  are  30  cm.  apart,  if  we  consider  only  the 
effect  of  the  adjacent  poles? 

4.  A  cylindrical  bar  magnet  is  2  cm.  in  diameter,  and  the  strength 
of  its  field  adjacent  to  the  end  of  the  magnet  is  800  gausses.     How 
many  maxwells  has  it  in  this  field? 

5.  A  bar  magnet  is  2  cm.  wide' and  8  mm.  thick.     Its  field  adja- 
cent to  the  end  has  1200"  maxwells.     What  is  the  strength  of  the  field 
in  gausses? 


CHAPTER  IX 


FIG.  293 


ELECTRICITY 

I.    STATIC   ELECTRICITY 

340.  Electrification.  —  Demonstrations.  —  Hold  a  warm,  dry 
glass  rod  over  a  handful  of  cork  filings,  pith  balls,  bits  of  paper,  etc., 
and  the  rod  will  not  affect  them.  Rub  the  rod  briskly  a  few  times 

with  a  piece  of  silk 
or  flannel,  and  the 
light  bodies  will 
begin  at  once  to  fly 
to  the  rod,  will  re- 
main there  for  an 
instant,  and  will 
then  fly  back  to 
the  table. 

Place  a  warm,  dry  sheet  of  glass  over  the  bits  of  paper,  supporting 
it  by  a  book  at  each  end.  No  effect  will  be  noticed  until  the  glass 
is  rubbed  with  the  silk,  when  the  bits  of  paper  will  at  once  begin  to 
jump  to  the  glass  and  back  again. 

Using  a  flannel  pad  for  a  rubber,  repeat  the  first  demonstration 
with  (1)  a  stick  of  sealing  wax,  (2)  a  rod  of  ebonite,  and  (3)  a  hard 
rubber  comb. 

The  above  demonstrations  show  that  when  glass  is  rubbed 
with  silk,  or  sealing  wax  with  flannel,  there  is  imparted  the 
property  of  attracting  light  bodies.  The  first  record  of  such 
a  phenomenon  was  made  by  the  Greeks  about  600  B.C.  Be- 
cause they  noticed  it  in  amber,  which  they  called  elektron, 
the  name  electricity  has  been  given  to  the  cause  of  these 

318 


STATIC   ELECTRICITY 


319 


FIG.  294 


phenomena,  and  a  body  that  is  capable  of  attracting  others 

in  this  way  is  said  to  be  electrified. 

i 
Demonstration.  —  Make  a  wire 

stirrup,  as  in  Fig.  294,  and  sus- 
pend in  it  a  wooden  rod  two  or 
three  feet  long.  Suspend  this  by 
a  s;lk  thread  from  a  support  and 
present,  near  one  end,  an  electri- 
fied glass  rod.  The  wooden  rod 
will  be  at  once  attracted.  Take 
out  the  wooden  rod,  suspend  the 
glass  rod,  and  present  the  end  of 
the  wooden  rod;  and  now  the 
glass  rod  moves.  Suspend  both 
rods,  and  they  move  toward  each 
other  until  they  touch. 

This  shows  that  the  action  that  takes  place  between  an 
electrified  and  an  unelectrified  body  is  mutual. 

341.  Two  Kinds  of  Electrification.  —  We  have  seen  that 
the  glass  rod,  the  sealing  wax,  and  the  ebonite  rod  all  attract 
other  bodies  when  electrified.  Their  action  upon  one  another 

may  be  seen  in  the 
following : 

Demonstration.  — 

Electrify  a  glass  rod 
and  suspend  it  in  the 
wire  stirrup.  Bring  a 
wooden  rod  near  it,  and 
it  will  be  attracted. 
Bring  an  electrified 
ebonite  rod  near  it,  and 
it  will  be  attracted  more 

than  before.     Now  electrify  a  second  glass  rod  and  bring  it  near 
the  end  of  the  suspended  rod,  and  repulsion  takes  place.    Suspend 


FIG.  295 


320  ELECTRICITY 

the  electrified  sealing  wax  in  the  stirrup  and  hold  near  it  a  second 
electrified  stick  of  sealing  wax,  and  repulsion  takes  place.  Hold 
near  it  an  electrified  glass  rod,  and  it  is  attracted.  Hold  near  it 
an  electrified  ebonite  rod,  and  it  is  repelled. 

We  find  that  the  electrified  glass  rod  and  sealing  wax 
have  apparently  the  same  effect  upon  an  unelectrified  body, 
but  act  differently  upon  one  that  is  electrified.  When  this 
difference  was  first  observed,  the  kind  of  electrification  pro- 
duced on  a  glass  rod  by  rubbing  with  silk  was  called 
vitreous  electricity,  and  that  produced  on  sealing  wax  by 
rubbing  it  with  flannel,  resinous  electricity.  These  are  now 
called  positive  or  +  and  negative  or  — ,  respectively.  For 
the  sake  of  convenience,  these  states  of  electrification  will 
be  spoken  of  as  positive  and  negative  electricity. 

342.  Action  of  Electrified  Bodies  upon  Each  Other.  —  Ex- 
periment   has  established    the  following  general    law  -con- 
cerning electrified  bodies : 

Bodies  charged  with  like  electricities  repel  each  other,  and 
those  charged  with  unlike  electricities  attract  each  other. 
Compare  this  with  the  first  law  of  magnetism  (§  322). 

Demonstration.  —  Cut  out  a  number  of  pith  balls  with  a  pen- 
knife and  roll  them  in  the  hands.  Use  the  pith  of  corn,  elder,  or, 
better  still,  burdock.  Suspend  one  of  them  from  a  bent  glass  rod 
by  a  fine  silk  thread.  Electrify  a  straight  glass  rod  and  bring  it 
near  the  ball,  which  will  at  once  be  attracted,  cling  to  the  rod  for 
an  instant,  and  then  fly  away  charged  with  a  +  charge.  Rub 
different  bodies,  such  as  a  dry  paper,  a  rubber  comb,  etc.,  first  with 
silk  and  then  with  flannel.  How  are  those  charged  that  repel  the 
ball  ?  If  a  body  attracts  a  charged  pith  ball,  is  it  a  proof  that  the 
body  is  charged? 

343.  Measure  of  Electrical  Attraction  and  Repulsion.  —  If 
two  minute  bodies  with  equal  charges  of  like  electricities 


STATIC   ELECTRICITY 


321 


when  one  centimeter  apart  in  air,  repel  each  other  with  a 
force  of  one  dyne,  each  charge  of  electricity  is  called  a  unit 
charge.  If  one  of  these  unit  charges  remained  the  same, 
the  other  would  need  to  be  increased  to  10  units  in  order  to 
increase  the  force  of  repulsion  to  10  dynes.  It  is  found  that 
the  force  of  electrical  repulsion  or  attraction  between  any 
two  small  electrified  bodies  varies  directly  as  the  product 
of  the  charges,  and  inversely  as  the  square  of  the  distance 
between  their  centers.  Hence 

/  =  ±  %  <51) 

in  which /is  the  force  in  dynes,  Q  and  q  the  electrical  charges 
of  the  bodies,  and  d  the  distance  between  their  centers  in 
centimeters.  By  reference  to  the  lawT 
of  mutual  action  (§  342)  it  will  be  seen 
that  the  +  sign  means  repulsion  and  the 
—  sign  attraction.  + 

344.  Electroscopes. — Any  instrument 

by  means  of  which  we  can   determine 

whether  bodies  are  charged  or  not  is  an 

electroscope.     A  pith  ball  arranged  as 

in  Fig.  296  is  a  pith-ball  electroscope.     A 

common  form  is  the  gold-leaf  electroscope, 
which  consists  of  a  glass  jar, 
through  the  wooden  stopper  of  which  passes  a 
brass  rod  terminating  in  a  ball  on  the  outside, 
and  having  two  long,  narrow  leaves  of  some  thin 
metal,  as  goldfoil,  attached  to  the  inner  end. 
Whenever  the  ball  is  touched  with  a  charged 
body  the  leaves  receive  a  part  of  the  same 

charge  and  diverge  in  accordance  with  the  law  of  repulsion 

(§  342),  as  shown  in  Fig.  297. 

Rev. 


FIG.  296 


FIG.  297 


322  ELECTRICITY 

For  convenience  in  using  an  electroscope,  a  proof  plane  may 
be  made  by  cementing  a  thin  metal  disk  to  the  end  of  a  rubber 
penholder  (Fig.  298).  Put  this  plane  in  contact  with  any 

•  charged  body,  remove  it,  and  quickly 

touch  the  knob    of    an  electroscope 


FIG.  298 

touch  it  with  the  proof  plane,  and  then  bring  the  plane  near 
the  knob  of  the  electroscope.  If  the  leaves  diverge  still 
more,  they  show  that  the  first  body  was  charged  positively. 
If  the  leaves  fall  together  somewhat,  it  is  probable  that 
the  body  was  charged  negatively;  but  as  the  repulsion  of 
the  leaves  is  the  only  sure  test,  the  proof  plane  must  be 
charged  negatively  from  sealing  wax  and  again  brought 
near  the  electroscope.  If  the  leaves  now  diverge,  the  first 
body  was  charged  negatively. 

345.  Conductors  and  Insulators.  —  Demonstration.  —  Wind 
one  end  of  a  copper  wire  a  meter  long  around  the  knob  of  an  elec- 
troscope, and  attach  a 
brass  ball  to  the  other 
end.  Rest  it  on  a  glass 
support.  Charge  the 
proof  plane  from  a 
charged  body  and  touch 
the  ball  with  it.  The 
leaves  of  the  electro-  FIG.  299 

scope  will  instantly  di- 

verge. Discharge  the  electroscope  by  touching  it  with  the  finger. 
Replace  the  wire  by  a  silk  thread,  and  no  effect  will  be  seen  when 
the  ball  is  charged.  Replace  the  silk  thread  by  a  damp  cotton 
thread,  and  the  leaves  will  diverge  gradually  when  the  ball  is 
charged. 

Bodies  like  the  wire,  which  carry  electrical  charges  readily, 
are  called  conductors;  while  those  like  silk,  which  carry  them 


STATIC  ELECTRICITY  323 

with  difficulty,  are  called  insulators,  nonconductors,  or  dielec- 
trics. There  are  no  substances  that  are  perfect  conductors, 
neither  are  there  any  that  are  perfect  insulators;  but  the 
following  table  gives  what  are  usually  classed  as  conductors 
and  insulators,  all  arranged  in  the  order  of  their  conductivity. 

CONDUCTORS  INSULATORS 

Metals,  Animals,  Dry  Wood,         Glass, 

Graphite,  Linen,  Dry  Air,  Ebonite, 

Acids,  Cotton  Paper,  Shellac. 

Salt  Water,  Silk, 

The  conductivity  of  bodies  depends  upon  their  physical 
condition,  temperature  and  moisture  having  a  decided  effect. 
Glass  becomes  a  conductor  at  200°  C.  Air  under  normal 
pressure  is  a  good  insulator,  rarefied  air  is  a  poor  one.  Pure 
water  is  a  very  poor  conductor,  but  is  rendered  a  good  con- 
ductor by  the  addition  of  a  little  salt  or  a  few  drops  of  acid. 
Whether  bodies  are  conductors  or  not  also  depends  upon  the 
character  of  the  electrical  charge.  A  single  layer  of  cotton 
is  insulation  between  two  wires  carrying  the  current  for  an 
electric  bell,  but  is  no  protection  whatever  against  the  sparks 
from  a  charged  glass  rod. 

346.  Friction  Develops  Both  Kinds  of  Electricity. — Demon- 
stration. —  Rub  a  glass  rod  and  an  ebonite  rod  together,  much  as  a 
mower  whets  his  scythe.  Test  each  by  bringing  it  near  the  knob  of 
an  electroscope.  The  glass  will  be  found  to  be  charged  positively 
and  the  ebonite  will  show  an  equal  negative  charge. 

Tests  carefully  made  by  rubbing  various  substances  to- 
gether show  not  only  that  both  kinds  of  electricity  are  pro- 
duced, but  also  that  the  opposite  charges  generated  are  equal 
in  amount.  For  instance,  the  +  charge  generated  upon  a 
glass  rod  is  the  same  in  quantity  as  the  —  charge  generated 
upon  the  silk  by  which  it  is  rubbed. 


324  ELECTRICITY 

347.  Can  Conductors  be  Electrified  by  Friction?  — If  a 
brass  tube  is  rubbed  with  either  silk  or  flannel  and  then 
tested  with  an  electroscope,  no  evidence  of  a  charge  will 
be  found.     This,  however,  is  not  a  proof  that  no  charge  is 
generated ;  for  any  charge  would  be  carried  away  by  the 
body  of  the  experimenter  as  fast  as  generated,  since  both 
the  rod  and  the  body  are  conductors. 

Demonstration.  —  Flip  a  silk  handkerchief  against  the  knob  of 
an  electroscope  and  the  leaves  will  be  found  to  separate.  The  glass 
body  of  the  electroscope  could  not  carry  away  the  charge  generated, 
by  the  friction  of  the  silk  on  the  brass  ball.  Determine  whether  the 
charge  is  positive  or  negative. 

Rub  a  glass  tube  an  inch  or  more  in  diameter  with  a  silk  pad. 
Present  the  knuckle  to  a  point  on  the  side,  and  take  off  a  spark.  Do 
this  at  various  points  along  the  tube.  Since  the  glass  is  a  noncon- 
ductor you  discharge  only  a  small  area  each  time. 

If  unlike  substances  are  pressed  together  and  then  rapidly 
separated,  they  will  become  oppositely  charged.  This  is 
seen  in  the  fact  that  sparks  can  be  drawn  from  a  leather  belt 
in  running  machinery,  especially  in  dry  weather. 

348.  Distribution  of  Electricity  over  a  Conductor.  —  If  a 

metal  sphere  is  placed  upon  an  insulating  support,  such  as 

a  glass  rod,  and  charged  with 
a  certain  quantity  of  elec- 
tricity, a  proof  plane  placed 
upon  any  part  of  its  surface 
will  carry  away  the  same 
charge,  as  may  be  found  by 
tests  with  an  electroscope 
(the  leaves  diverging  as  much 

from  one  charge  as  from  another).     But  if  an  equal  charge 
is  given  to  an  insulated  metal  cylinder  with  rounded  ends, 


STATIC   ELECTRICITY  325 

the  proof  plane  will  carry  a  much  greater  charge  away  from 
the  ends  than  from  any  other  part  of  the  surface.  The 
comparative  density  of  charge,  or  quantity  of  charge  per  unit 
area,  is  represented  by  the  distance  of  the  dotted  line  from  the 
surface  in  Fig.  300.  From  this  it  appears  that  the  density 
of  charge  is  greater  at  the  projecting  parts  of  an 
insulated  conductor. 

Demonstration.  —  Support   a    short   metal   cylinder 
upon  an  insulating  stand.     Fasten  a  wire  3  in.  long  ver- 
tically into  the  top  of  the  cylinder.     From  the  top  of 
this  wire   suspend  two   pith   balls  by    linen    threads. 
Suspend  two   others  from  the  inside  of  the  cylinder. 
Charge  the  cylinder  with  the  charge  from  a  glass  rod ;     FlG'  301 
the  outer  pair  of  balls  will  fly  apart,  while  the  inner  ones  will  remain 
undisturbed. 

From  this  we  learn  that  on  an  insulated  conductor  the  elec- 
trical charge  is  located  on  the  outside.  This  location  is  caused 
by  the  mutual  repulsion  of  like  charges.  It  follows  that, 
with  the  same  charge,  as  the  outside  surface  increases  the 
surface  density  diminishes. 

349.  The  Action  of  Points.  — Demonstration.  — Fix  a  pin,  at 
its  middle,  to  the  end  of  a  stick  of  sealing  wax,  which  serves  as  an. 
insulator.  Charge  an  electroscope  until  the  leaves  are  widely  sepa- 
rated. Place  the  head  of  the  pin  against  the  knob,  and  observe  that, 
the  leaves  gradually  fall  together.  Hold  a  pin  in  the  hand  and  bring 
its  point  near  the  knob  of  a  charged  electroscope.  What  happens  ? 

If  the  experiment  with  pin  and  sealing  wax  is  made  upon 
a  body  with  a  much  greater  charge  than  the  electroscope, 
a  decided  current  of  air  can  be  felt  in  front  of  the  point. 
The  density  of  the  charge  at  the  point  electrifies  the  air  par- 
ticles, which,  by  the  law  of  repulsion,  are  at  once  driven  off. 
As  each  particle  takes  its  own  charge  away,  it  follows  that  a 


326  ELECTRICITY 

body  with  pointed  surfaces  cannot  be  kept  charged,  however 
good  the  insulation. 

350.  Electrical  Potential.  —  Demonstration.  —  Charge  two  in- 
sulated conductors  —  tin  cans  upon  glass  tumblers  will  do  —  with 
the  glass  rod,  and  connect  one  of  them  with  a  gold-leaf  electroscope 
by  means  of  a  piece  of  wire  provided  with  an  insulating  handle. 
Notice  the  extent  to  which  the  leaves  separate.  Remove  the  wire 
from  the  body  and  discharge  the  electroscope.  Connect  the 
electroscope  with  the  second  body,  and  notice  the  divergence  of  the 
leaves.  Now  connect  the  two  charged  bodies  by  a  conductor  and 
notice  that  if  the  divergence  of  the  leaves  of  the  electroscope  was 
less  when  connected  with  the  second  body  than  when  connected 
with  the  first,  they  will  now  diverge  more  widely  than  before  when 
connected  with  the  second,  and  vice  versa.  On  connecting  the  elec- 
troscope with  the  first  body  it  will  be  found  to  give  the  same  diver- 
gence as  the  second. 

From  this  demonstration  we  conclude  that  there  has  been 
a  flow  of  electricity  from  the  body  giving  the  greater  diver- 
gence of  the  gold  leaves  to  the  other.  This  condition  of  elec- 
trified bodies  which  sets  up  an  electric  current  in  a  conductor 
which  connects  the  two  bodies  is  the  difference  of  potential 
or  the  P.  D.  of  the  bodies. 

If  the  electrified  body  connected  with  the  electroscope 
is  now  connected  with  the  earth,  the  leaves  will  at  once  fall 
together,  showing  that  the  electroscope  is  discharged.  The 
quantity  of  electricity  in  the  body  is  so  small  that  it  does  not, 
on  being  connected  with  the  earth,  change  the  condition  of 
the  earth  in  any  perceptible  degree.  The  earth  is  —  for  the 
sake  of  reference  —  assumed  as  the  zero  of  potential,  bodies 
positively  charged  being  considered  at  a  higher  potential 
than  the  earth,  while  those  negatively  charged  are  at  a  lower 
potential  than  the  earth.  If  the  difference  of  potential 
between  two  bodies  is  kept  constant,  the  current  passing 


STATIC  ELECTRICITY  327 

in  the  conductor  that  joins  them  will  be  a  continuous  current. 
If  the  P.  D.  is  not  maintained,  the  current  will  be  only 
momentary. 

Potential  is  analogous  to  water  pressure,  and  the  current 
to  the  flow  of  water  that  takes  place  in  a  pipe  connecting 
two  bodies  of  water  at  different  levels.  The  position  of  the 
water  of  a  water  tank  with  respect  to  the  surface  of  the  earth 
would  be  positive :  the  water  would  run  from  the  tank  to 
the  earth.  The  position  of  the  water  in  a  well  would  be 
negative :  the  water  would  flow  from  the  surface  into  the 
well. 

351.  Capacity.  —  If  two  insulated  conductors,  of  the  same 
shape  but  of  different  sizes,  are  charged  to  the  same  potential, 
it  will  be  found  that  the  larger  one  has  a  greater  charge  than 
the  other.  This  means  that  there  is  a  difference  in  their 
electrical  capacity.  The  capacity  of  a  conductor  is  the  ratio 
of  its  quantity  of  charge  to  its  potential ;  that  is, 

C^f,  (52) 

in  which  C  =  capacity,  Q  =  number  of  units  of  electrifica- 
tion, and  V  =  number  of  units  of  potential. 

The  word  capacity  as  used  in  electricity  has  a  meaning 
different  from  that  usually  given  to  it.  We  say  that  the 
capacity  of  a  gallon  jug  is  4  quarts,  meaning  when  it  is  full. 
From  Formula  52,  we  see  that  the  capacity  of  a  conductor 
is  equal  numerically  to  the  quantity  of  electricity  on  it 
when  its  potential  is  I  unit.  The  quantity  that  a  gallon  jug 
can  hold  is  never  greater  than  its  capacity  —  4  quarts ;  but 
the  number  of  units  of  charge  that  can  be  given  to  an  insu- 
lated conductor  may  be  many  times  its  capacity,  in  which 
case  its  potential  will  be  many  times  1  unit,  Since  electricity 


328  ELECTRICITY 

in  its  static  condition  is  on  the  outside  of  bodies,  a  wooden 
ball  covered  with  metal  foil  has  the  same  capacity  as  a  solid 
metal  ball  of  the  same  size. 

352.  Induction.  —  Demonstration,  —  Bring  an  electrified  glass 
rod  near  the  knob  of  an  electroscope,  and  the  leaves  will  begin  to 
diverge  when  the  rod  is  a  foot  or  more  away.     Bring  it  nearer,  and 
the.  divergence  is  greater.     Remove  the  rod,  and  the  leaves  fall 
together. 

We  learn  from  this  that  the  influence  of  the  charged  rod 
extends  to  some  distance  through  the  air.  This  action  of  a 
charged  body  upon  another  body  in  the  electrical  field  which 
surrounds  it,  is  called  electrostatic  induction. 

353.  To  Charge  a  Body  by  Induction.  —  In  the  preceding 
demonstration    we    notice    that    the    electroscope    remains 
charged  only  so  long  as  the  inducing  body  is  near  it.     It  is 

possible,  however,  to  charge  the 
electroscope  permanently,  as  fol- 
lows: 


Demonstration. — Bring  the  glass 
rod  near  the  knob  as  before,  and 
when   the    leaves    have    separated, 
3Q2  touch  the  knob  with  the  finger.     The 

leaves  instantly  fall  together.     Now 

remove  first  the  finger  and  then  the  rod,  and  the  leaves  again  di- 
verge, showing  that  the  electroscope  has  received  a  permanent 
charge. 

To  explain  this  action  we  must  remember  that  like  elec- 
tricities repel,  and  unlike  electricities  attract  each  other.  When 
the  electrified  rod  is  brought  near  the  knob,  the  +  of  the  rod 
separates  the  electricities  in  the  knob,  wire,  and  leaves  of 
the  electroscope,  driving  the  like  kind,  +,  to  the  leaves, 
and  holding  the  unlike  kind,  — ,  near  to  itself  in  the  knob 


STATIC   ELECTRICITY 


329 


FIG.  303 


as  in  Fig.  302.  When  the  knob  is  touched  it  is  put  in  contact 
with  the  earth,  and  the  +  electricity,  repelled  by  the  -f  of  the 
rod,  escapes,  while  the 
—  is  held  bound.  Fig- 
ure 303  shows  this  condi- 
tion. Figure  304  shows 
tire  condition  when  the 
contact  with  the  earth 
is  broken  and  then  the 
glass  rod  is  removed. 
The  —  electricity  is  no 
longer  bound,  but  free,  and  so  passes  partly  from  the  knob 
into  the  wire  and  leaves,  which  diverge  less  than  before,  but 

with  a  charge  of  —  electricity. 

From  this  we  see  that  a  body  can  be  charged 

by  induction,  if  only  some  way  is  provided  by 

which  to  carry  off  the  electricity  that  is  repelled 

by  the  inducing  body. 

The   inductive   action   of  a  charged  body  is 

well  shown  in  an  experiment  first  made  by 
Faraday,  called  the  ice-pail  experiment  because  he  used  ice 
pails  in  making  it : 

Demonstration.  —  Place  a  thin 
metallic  vessel,  like  a  tin  can,  upon 
an  insulating  stand  and  connect  it  by 
a  wire  with  the  knob  of  an  electro- 
scope. Suspend  a  positively  charged 
metal  ball  by  a  silk  thread  and  lower 
it  within  the  can;  the  leaves  at  once 
diverge.  Remove  the  ball,  and  they  fall  together.  Lower  the  ball 
again,  and  they  diverge.  Touch  the  can,  and  they  fall.  Remove 
the  finger  and  then  the  charged  ball  and  the  leaves  separate, 
charged  with  negative  electricity.  Explain. 


FIG.  304 


FIG.  305 


330  ELECTRICITY 

Discharge  the  electroscope  and  again  lower  the  ball.  Observe 
the  amount  of  divergence  of  the  leaves.  Let  the  ball  touch  the  inside 
of  the  can.  Notice  that  the  divergence  of  the  leaves  is  not  changed. 
Remove  the  ball,  and  the  leaves  will  still  be  separated,  charged  with 
positive  electricity.  Explain. 

A  thorough  study  and  understanding  of  the  above  experi- 
ment will  give  the  student  a  correct  idea  of  the  phenomena 
of  induction. 

The  attraction  of  an  unelectrified  body  by  an  electrified  one  is  the 
direct  result  of  induction.  The  positive  electricity  on  a  charged 
glass  rod  repels  the  positive  electricity  of  a  pith  ball  and  attracts 
the  negative.  Since  the  distance  between  the  positive  charge  on  the 
pith  ball  and  the  glass  rod  is  greater  than  the  distance  between  the 
negative  charge  and  the  rod,  the  repulsion  is  less  than  the  attraction, 
and  the  pith  ball  is  attracted. 

354.  Specific  Inductive  Capacity.  —  The  quantity  of  elec- 
tricity that  can  be  given  to  a  body  by  induction  depends 
upon  the  extent  of  its  surface,  the  distance  between  it  and 
the  inducing  body,  and  the  character  of  the  dielectric  that 
separates  them.  The  property  that  dielectrics  have  of  trans- 
mitting electrical  induction  is  called  their  specific  inductive 
capacity.  The  specific  inductive  capacity  of  air  is  taken 
as  unity,  and  that  of  a  few  other  substances  is  shown  in  the 
following  table : 

Air 1.00  Shellac      .     ...    2.75 

Paraffin      .     .     .    2.00  Ebonite    .     .     .    3.40 

India  Rubber      .     2.25  Glass   ....    6.25 

Demonstration.  —  Suspend  a  charged  ball  at  a  fixed  distance 
above  the  knob  of  an  electroscope  and  observe  the  divergence  of  the 
leaves.  Introduce  between  the  ball  and  the  knob  a  cake  of  paraffin, 
or  a  plate  of  glass,  first  making  sure  that  it  is  not  electrified,  and 
notice  the  change  in  the  divergence  of  the  leaves. 


STATIC  ELECTRICITY 


331 


355.  The  Electrophorus  is  a  simple  and  inexpensive  in- 
strument for  generating  an  electric  charge,  and  is  more  con- 
venient than  the  glass  rod  and 
silk  pad.  It  consists  of  a  glass 
plate  resting  upon  a  metal 
plate,  as  in  the  lower  part  of 
Fig.  306,  and  of  a  disk  of  brass 
or  other  metal  with  an  insulat- 
ing handle  H.  To  generate  a 

,  ,11  i    .      'j.  FIG.  306.  —  Electrophorus 

charge  upon  the  glass  plate  it 

is  rubbed  with  silk ;  this  gives  it  a  positive  charge.  The  brass 
plate  is  then  placed  upon  the  glass ;  since  the  surface  of  the 
glass  is  uneven,  there  is  a  thin  layer  of  air  between  them 
except  at  a  few  points  of  contact,  and  hence  the  disk  be- 
comes charged  by  induction  as  shown  in  (a),  Fig.  307.  The 
upper  surface  of  the  disk  is  now  touched  with  the  finger, 
and  the  free  positive  charge  escapes,  as  in  (b).  When  the 


(.0.) 


(b) 

FIG.  307.  —  Operation  of  the  Electrophoius 


disk  is  lifted  by  the  insulating  handle,  the  negative  charge, 
which  was  held  bound  by  the  positive  of  the  glass,  becomes 
distributed  over  the  entire  surface,  as  in  (c),  and  may  be  taken 
off  as  a  spark.  The  disk  may  then  be  at  once  replaced  on 
the  glass,  touched  with  the  finger,  and  removed,  and  another 
spark  of  practically  equal  length  obtained. 

When  the  disk  is  lifted,  work  is  done  not  only  against 


332  ELECTRICITY 

gravity  but  also  against  the  attraction  between  the  negative 
charge  on  the  disk  and  the  positive  on  the  plate.  The  energy 
of  the  discharge  that  can  be  taken  from  the  electrophorus 
is  given  to  it  by  the  work  that  is  done  against  this  electrical 
attraction,  and  by  the  law  of  conservation  of  energy  the 
amount  of  this  energy  is  equivalent  to  the  work  done. 

If  a  positive  charge  is  desired  instead  of  a  negative,  the 
glass  plate  is  replaced  by  one  of  ebonite  or  wax. 

356.  Condensers.  —  The  principle  -of  induction  is  used 
to  give  to  a  body  a  much  greater  charge  than  it  would  other- 
wise receive. 

Demonstration.  —  Cut  out  a  sheet  of  tin  foil  six  inches  square 
and  place  it  in  the  middle  of  a  pane  of  glass  a  foot  square.  Count 
the  number  of  sparks  that  you  can  make  pass  from  the  electrophorus 
disk  to  the  square  of  tin  foil.  Discharge  the  tin  foil  by  touching  it. 
Lift  the  glass  plate  from  the  table  and  place  under  it  a  second  sheet 
of  tin  foil  connected  with  the  earth.  Count  the  number  of  sparks 
that  you  can  now  make  pass  into  the  upper  tin  foil.  Touch  the 
—  _i_  lower  tin  foil  with  one  hand,  and  the 

Q  O    upper  tin  foil  with  the  other.     How  does 

the  spark  differ  from  the  ordinary  ? 


The  simple  instrument  used  in  the 
above  demonstration  contains  all  that 
is  essential  in  a  condenser,  namely, 
two  conductors  separated  by  a  dielec- 
tric. The  reason  for  using  a  con- 
denser is  that  we  may  increase  the 
quantity  of  electricity  without  in- 
FIG.  308  creasing  the  potential.  The  quantity 

of  electricity  that  can  be  stored  on  each  conductor  is  directly  pro- 
portional to  its  area  and  inversely  proportional  to  the  thickness 
of  the  dielectric  between  the  conductors.  The  reason  for  the 


STATIC  ELECTRICITY  333 

action  of  the  condenser  follows  from  §  353.  A  convenient 
form  of  condenser  of  large  capacity  can  be  made  by  arranging 
two  sets  of  sheets  of  tin  foil  as  in  Fig.  308,  and  separating  them 
by  putting  sheets  of  mica,  or  paper  soaked  in  melted  paraffin, 
between  them. 

357.  The  Leydea  Jar  is  a  convenient  form  of  condenser. 
It  consists  of  a  glass  jar  with  a  wooden  stopper,  through 
which  passes  a  brass  rod 
terminating  outside  in  a 
metal  ball  and  inside  in 
a  chain  touching  the  inner 
coating  of  the  jar. 
jar  is  coated  both  inside 
and  outside,  to  about  two 
thirds  its  height,  with  tin 
foil  pasted  on  the  glass. 
The  jar  should  be  made  of 
thin  glass,  to  give  it  greater 
capacity,  but  if  the  glass  is 

tOO  thin,   it  is  liable  to  be       FIG.  309.  — Discharging  a  Leyden  Jar 

pierced  by  a  heavy  charge. 

The  Leyden  jar  is  charged  by  holding  it  in  the  hand,  or  in 
some  other  way  connecting  the  outer  coating  with  the  earth, 
and  presenting  the  ball,  connected  with  the  inner  coating, 
to  the  source  of  electricity.  It  is  discharged  by  touching 
the  outside  coating  with  one  end  of  a  discharger  and 
bringing  the  other  end  near  the  knob  of  the  jar,  when  the 
discharge  will  take  place  in  the  form  of  a  heavy  spark, 
as  in  Fig.  309.  The  outer  coating  should  be  touched  by 
the  discharger  first,  or  the  heavy  spark  will  tear  off  the  tin- 
foil coating. 


334 


ELECTRICITY 


358.  Seat  of  the  Charge.  —  If  the  discharger  is  used  again 
a  short  time  after  a  jar  has  been  discharged,  a  second  and 
much  fainter  discharge  takes  place.  This 
could  not  be  the  case  if  the  charge  were 
located  in  the  conducting  coatings,  as 

A  \  I       lf«lliU    they  would  be  discharged  at  once. 


Procure  a  Leyden  jar  with  movable  coatings, 
which  consists  of  a  cone-shaped  glass  jar,  A 
in  Fig.  310,  having  two  conical  tin  coatings, 
one,  B,  fitting  the  inside,  the  other,  (7,  the 
outside  of  the  glass.  Put  the  parts  together 
FIG.  310  and  charge  the  jar.  Remove  the  inner  coat- 

ing with  a  glass  rod  and  bring  it  near  an 
electroscope.  It  will  be  found  to  have  no  charge.  Remove  the 
outer  coating  and  test  in  the  same  way.  It  has  no  charge.  Now 
put  the  jar  together  again,  and  a  spark  can  be  taken  from  it  by 
connecting  the  inner  and  outer  coatings. 

These  results  prove  that  the  coatings  act  simply  as  a 
means  for  collecting  the  charge,  and  that  the  seat  of  the 
charge  is  in  the  glass.  As  the 
glass  is  a  poor  conductor,  the 
charge  does  not  all  pass  into 
the  coatings  at  once,  when  the 
jar  is  discharged.  This  explains 
the  second  spark,  which,  is  called 
the  residual  discharge. 

359.  Battery  of  Leyden  Jars. 
— The  method  usually  employed 
to  secure  large  capacity  with 

T        ,  .  FIG.  311.  — Leyden  Jars 

Leyden  ]ars  is  to  connect  the 

outer  coatings  of  a  number  of  jars  to  the  earth  or  to  one  ter- 
minal of  an  electrical  machine,  and  the  inner  coatings  to  the 


STATIC   ELECTRICITY 


335 


other  terminal.  In  this  way  the  surface  is  increased,  and  a 
greater  quantity  of  electricity  can  be  stored.  The  spark 
from  such  a  battery  is  much  thicker  than  one  of  the  same 
length  from  a  single  jar. 

360.  Electrical  Machines ;  Frictional  Machines.  —  In  the 
early  forms  of  electrical  machines  the  charge  was  developed 
directly  by  friction.     The  most  convenient  of  these  was  the 
plate  machine,  which  consisted  chiefly  of  a  glass  disk  mounted 
upon  an  axis  and  turned  by  a  handle,  the  charge  being  pro- 
duced by  the  friction  of  fixed  rubbing  pads.     On  account  of 
the  friction,  this  machine  required  a  great  deal  of  energy  to 
run  it,  and  partly  for  this  reason  it  has  nearly  gone  out  of  use. 

361.  Induction  Machines.  —  The  simplest  form  of  the  in- 
duction machine  is  the  electrophorus  (§  355).     In  fact,  a 


FIG.  312.—  Toepler-Holtz  Electrical  Machine 

large  induction  machine  may  be  considered  a  continuous 
Many  forms  of  induction  machines  are   in 


336  ELECTRICITY 

use.  In  the  Toepler-Holtz  machine  there  is  a  fixed  glass 
disk  called  the  field  plate,  having  pasted  upon  the  back  side 
four  tin-foil  disks,  T,  connected  two  and  two  by  strips  of 
tin  foil  covered  with  large  sectors  of  paper.  These  inductors 
correspond,  one  pair  to  the  glass  plate  of  an  electrophorus 
(being  charged  positively),  and  the  other  to  the  ebonite 
plate  of  another  electrophorus  (charged  negatively).  In 
front  of  the  field  plate  is  a  second  glass  disk,  which  rotates 
upon  an  axis.  On  the  front  face  of  this  disk  there  are  pasted, 
at  equal  intervals,  six  tin-foil  disks,  to  the  centers  of  which 
there  are  cemented  metal  buttons.  These  correspond  to 
the  brass  disk  of  an  electrophorus.  A  fixed  rod,  with  a  metal 
comb  at  each  end,  crosses  diagonally  from  A  to  B  in  front 
of  the  movable  plate,  and  fulfills  the  function  of  the  finger 
that  touches  the  electrophorus  disk.  The  two  kinds  of 
electricity  are  taken  off  by  collecting  combs  on  opposite  sides, 
connected  with  two  rods  which  have  at  their  outer  ends 
insulating  handles,  K  and  Kf,  and  on  the  inner  ends  brass 
balls,  the  terminals  between  which  the  discharge  takes  place. 
A  brighter  spark  may  be  obtained  by  connecting  a  Leyden 
jar  to  each  terminal,  as  shown  in  the  figure. 

The  machine  is  first  charged  by  setting  the  rotating  plate  in 
motion  and  then  sending  a  spark  of  +  electricity  from  a  charged 
glass  rod  to  one  of  the  inductors  on  the  back  of  the  stationary  plate, 
for  example,  on  the  right-hand  side  in  the  figure.  This  induces  a 
—  charge  in  and  near  disk  A  on  the  rotating  plate,  and  through  the 
diagonally  fixed  rod  a  +  charge  is  repelled  to  disk  B.  As  the  plate 
rotates,  disk  A  is  carried  to  the  left,  and  the  metal  button  on  it  is 
brought  into  contact  with  a  small  metal  brush  attached  to  C,  an  arm 
connected  with  the  inductor  on  the  left  side  of  the  field  plate.  A 
part  of  the  —  charge  of  disk  A  passes  over  to  that  inductor,  the 
remainder  is  repelled  by  the  —  inductor  into  the  collecting  comb 
connected  with  K,  and  when  this  disk  A  reaches  the  position  marked 


STATIC   ELECTRICITY 


337 


B,  it  is  charged  positively  by  the  direct  influence  of  the  left-hand 
inductor  combined  with  the  indirect  influence  of  the  other  inductor, 
as  explained  at  the  beginning.  Meanwhile  the  original  disk  B  has 
given  up  part  of  its  +  charge  to  the  right-hand  inductor  through  C', 
and  the  rest  to  the  collecting  comb  connected  with  K',  and  at  posi- 
tion A  is  receiving  a  —  charge  by  induction,  in  the  same  way  that  the 
disk  at  B  is  receiving  a  +  charge. 

The  terminals  should  be  put  in  contact  until  a  hissing  sound  shows 
that  the  machine  is  highly  charged.  When  they  are  separated,  a 
series  of  sparks  will  pass  from  one  terminal  to  the  other.  Examine 
the  two  sides  of  the  machine  with  a  pith-ball  electroscope  to  see 
which  is  +  and  which  — .  Discharge  it,  start  over  again,  using  a 
spark  from  a  stick  of  sealing  wax  to  charge  the  first  inductor,  and 
examine  with  pith-ball  electroscope  as  before. 

362.  The  Spark.  —A  little  study  of  the  sparks  that  pass 
between  the  terminals  will  show  that  the  polarity  of  the 
machine   determines   the   appearance   of   the    spark.     The 
main  spark  is  purple  in  color,  and  the  ends  differ  according 
to  their  polarity,  the  negative 

end  being  a  minute  bright 
point,  while  the  positive  end  is 
not  so  bright ;  the  bright  part, 
however,  is  longer,  being  about 
an  eighth  of  an  inch  in  an  inch 
spark. 

363.  The   Wimshurst    Ma- 
chine has  two  glass  disks,  both 
of  which  rotate,   but   in   op- 
posite directions.    Tin-foil  sec- 
tors are  attached  to  the  outside 
of    each   plate.     For  conven- 
ience in  explaining  the  action  of  this  machine,  in  Fig.  314 
the  glass  disks  are  replaced  by  glass  cylinders,  one  inside  the 

Rev. 


FIG.  313. — Wimshurst  Machine 


338 


ELECTRICITY 


T+ 


FIG.  314 


other,  and  shown  in  section.     A  A'  and  BB'  are  the  cylin- 
ders, the  sectors  on  A  A'  being  on  the  outside,  and  those  on 

BB'  being  on  the  inside,  CC' 
and  DD'  are  the  diagonal 
rods,  tipped  with  brushes; 
and  EE'  and  FF'  are  the  col- 
lecting brushes.  Only  the 
slightest  difference  of  poten- 
tial is  needed  to  start  the  in- 
duction. Suppose  the  sectors 
near  A  to  have  a  slight  + 
charge.  This  will  induce  a 
—  charge  on  C,  while  the  repelled  +  will  go  to  C".  The  sec- 
tors that  come  in  contact  with  the  brushes  on  C  and  C'  will 
receive  slight  charges  which  will  in  turn  act  inductively  on 
the  outer  sectors;  the  rod  DD'  acting  like  the  rod  CC". 
At  the  collecting  brushes  E  and  E'  the  —  charge  on  each 
cylinder  repels  that  on  the  other  to  E  and  Ef  and  the  ter- 
minal T1 '.  In  a  similar  way  a  +  charge  collects  on  T. 

364.  The  Effects  of  the  Discharge  from  a  Leyden  jar  or 
from  an  electrical   machine,  include   (a)  mechanical  work, 
(6)  heat,  and  (c)  light. 

365.  Mechanical    Effects.  —  Dem- 
onstrations.— Hold  a  thick  card  between 
the  terminals  of  a  Holtz  or  Wimshurst 
machine  when  it  is  connected   with  the 
condensers,  and  set  the  machine  in  action. 
A  spark  will  pass,  and  since  the  card  is 
a  nonconductor,  the  spark  will  tear  its 
way  through. 

Set  a  wire  upright  in  a  wooden  base,  and  file  its  upper  end  to  a 
point.     Place  over  this  wire  a  thin  test  tube,  as  in  Fig.  315,  and  bring 


FIG.  315 


STATIC  ELECTRICITY  339 

one  terminal  of  the  machine  directly  over  it.  Connect  the  wire 
with  the  other  terminal,  and  attach  the  Leyden  jars.  When  the 
machine  is  put  in  operation,  a  spark  will  pass  and  pierce  the  tube. 
If  the  tube  is  a  thick  one,  several  sparks  may  go  from  point  to  knob 
over  the  surface  of  the  glass  before  it  is  pierced. 

Any  nonconductor,  if  not  too  thick,  can  be  pierced  by 
the  condenser  spark  between  the  terminals  of  the  machine. 
Cardboard,  books,  seasoned  wood,  etc.,  should  be  tried. 
Try  a  metal  plate  also.  Is  it  pierced  ?  Explain. 

366.  Heat  Effects.  —  The  amount  of  current  that  passes 
when  a  charged  body  is  discharged  through  a  conductor 
is  but  small,  and  the  heating  of  the  conductor  is  conse- 
quently little.     When  the  discharge  takeL   place  through 
a  nonconductor,  however,  the  effect  is  much  greater.     The 
spark  itself  is  evidence  of  this,  since  in  this  case  enough 
heat  is  given  off  to  produce  light.    The  spark  is  sometimes 
used  to  light  the  gas  in  buildings  where  the  chandeliers  cannot 
be  readily  reached. 

Demonstration.  — •  Bring  a  gas  jet  between  the  terminals  of  a 
machine.  Operate  the  machine  until  the  sparks  pass,  and  then  turn 
on  the  gas.  It  is  lighted  at  once.  Why? 

367.  Light  Effects.  —  The  light  effects  of  the  discharge 
can  best  be  studied  at  night,  though  a  room  that  can  be 
made  nearly  dark  with  curtains  will  do.     In  the  first  place, 
the  machine  itself  affords  excellent  illustrations  of  these  ef- 
fects.   The  shower  of  purple  sparks  that  follow  one  another  so 
rapidly  that  the  images  of  six  or  eight  are  continually  seen,  — 
the  sharp  spark  of  the  condenser  discharge,  which  makes 
everything   dazzlingly   bright,    and   which   takes   place   so 
quickly  that  the  rapidly  rotating  wheel,  as  seen  by  its  light, 
seems  to  stand  still,  —  the  cascade  of  minute  sparks  that 


340  ELECTRICITY 

flows  over  the  plate  near  the  collecting  combs,  —  and  the 
glow  of  light  that  tips  every  point  of  the  combs,  —  all  are 
light  effects  of  the  most  interesting  kind. 

Demonstration.  —  Cover  one  side  of  a  dry  white  pine  board  with 
a  heavy  coat  of  shellac.  Next  place  on  this  a  layer  of  thin  tin  foil 
and  cover  this  with  shellac,  rubbing  it  down  fast  to  the  board.  Dry 
thoroughly  and  then  with  a  sharp  knife  cut  the  tin  foil  into  squares 
a  quarter  of  an  inch  on  a  side.  Connect  the  tin  foil  at  the  ends  of  the 
board  with  the  terminals  of  the  machine,  and  the  discharge  will  be 
seen  to  pass  the  entire  length  of  the  tin  foil,  causing  a  spark  at  every 
place  where  the  conductor  has  been  cut. 

Such  boards  can  be  made  in  any  desired  shape;  they 
illustrate  the  fact  that  if  a  discharge  takes  place  along  a 

broken  conductor  a  spark 
will  occur  at  every  gap. 

Demonstration.  — Get  a 
piece  of  No.  30  magnet  wire 
and  with  a  knife  or  pair  of 
cutting  pliers  cut  the  wire 
every  half  inch  without  cut- 
ting the  insulation.  Sus- 
pend this  from  the  ends 
over  the  terminals  of  the 
machine,  and  when  the  ma- 
chine is  put  in  motion  every  break  in  the  wire  will  furnish  a  bright 
spark.  The  insulation  will  hold  the  pieces  of  wire  in  place,  and 
they  can  be  made  into  many 
fanciful  shapes. 


368.  The  Brush  Dis- 
charge is  another  very  in-  FlG- 3l7-  ~  Brush 
teresting  light  effect.  It  is  obtained  by  drawing  the  termi- 
nals of  a  machine  two  or  three  inches  apart.  The  distinct 
sparks  will  then  cease  and  the  discharge  will  take  the  form 


STATIC  ELECTRICITY  341 

of  Fig.  317.  Near  the  positive  terminal  the  discharge  is 
bright,  like  an  ordinary  spark,  but  about  half  an  inch  away 
it  branches  out  and  becomes  a  purple  glow  until  the  negative 
pole  is  reached,  where  there  are  a  number  of  bright  points. 

369.  The  Discharge  in  Rarefied  Gases. — The  electric 
discharge  that  takes  place  in  the  air  at  ordinary  pressure 
gives  rise  to  a  bright  light  and  a  sharp  report.     If  the  dis- 
charge takes  place  in  a  partial  vacuum,  however,  the  light  is 
very  much  softened  and  the  discharge  is  silent. 

Demonstration.  —  Hold  the  bulb  of  an  incandescent  lamp  be- 
tween the  terminals  of  a  Holtz  or  Wimshurst  machine,  and  set  the 
machine  in  motion.  The  lamp  will  be  filled  with  a  pale  glow, 
which  will  come  and  go  in  flashes  as  long  as  the  machine  is  turned. 
The  discharge  in  rarefied  gases  is  studied  further  in  §  445. 

370.  The  Discharge  of  the  Leyden  Jar  Oscillatory.  —  Ex- 
periments show  that  the  discharge  of  a  condenser  is  an  oscil- 
lation,  the   charge   going   first   in   one 

direction  and  then  in  the  other.  This  is 
analogous  to  what  will  take  place  in  a 
U-tube,  such  as  is  shown  in  Fig.  318,  if 
it  is  filled  with  water  in  the  two  arms  to 
the  points  A  and  B.  If  now  the  clamp 
at  C  is  suddenly  opened,  the  water  will 
flow  from  the  left  side  to  the  right,  and 
instead  of  stopping  at  the  level  line  xy 
will  pass  on  to  D  and  E.  The  same  thing 
now  takes  place  in  the  opposite  direction,  and  so  continues  al- 
ternating until  the  water  finally  comes  to  rest  at  the  level  xy. 

371.  Atmospheric  Electricity.  —  No  one  who  has  observed 
both  the  discharge  of  frictional  electricity  and  lightning  has 
failed  to  notice  the  similarity  between  them.     Their  identity 


342 


ELECTRICITY 


was  proved  by  Franklin  in  1752.  His  method  of  proof  was 
one  that  would  not  be  followed  at  the  present  time  on  account 
of  the  danger  to  the  experimenter.  What  he  did  was  to  fly  a 


FIG.  319.  —  Lightning 


FIG.  320.  —  Condenser  Discharge 


kite  in  the  face  of  an  advancing  thunderstorm.  A  pointed 
wire  was  fastened  to  the  top  of  the  kite,  and  a  short  strip 
of  silk  was  tied  to  the  kite  string.  At  the  junction  between 
the  kite  string  and  the  silk  strip  a  door  key  was  tied.  As 
long  as  the  kite  string  was  dry,  no  results  were  obtained, 
but  as  soon  as  it  became  wet  with  the  rain  (making  it  a 
better  conductor),  Franklin  found  it  possible  to  draw  sparks 
from  the  key  by  bringing  his  finger  near  it. 

372.  How  Clouds  become  Charged.  —  Experiment  has 
proved  that  if  water  is  allowed  to  fall  upon  a  rising  cur- 
rent of  air  that  is  rapid  enough  to  break  it  into  drops,  the 
drops  become  positively  and  the  air  negatively  charged. 
It  is  well  known  that  the  formation  of  the  cumulus  cloud, 
called  a  thunder  head,  is  caused  by  an  uprush  of  warm, 
vapor-laden  air  into  the  cooler  upper  atmosphere.  This 


STATIC  ELECTRICITY  343 

gives  rise  to  a  turbulent  condition  in  the  clouds,  which  seem 
to  be  "  boil  ing,"  or  rolling  over  and  through  each  other,  and 
sets  up  such  a  condition  that  the  raindrops  formed  become 
electrically  charged. 

373.  Lightning.  —  This  high  potential  positive  charge  in 
the  clouds  induces  a  negative  charge  in  the  earth  beneath, 
and  as  soon  as  the  difference  of  potential  between  them  be- 
comes great  enough,  the  spark,  or  lightning  flash,  breaks 
through  the  air,  taking  the  path  of  least  resistance,  and 
generally  striking  a  tree  or  some  other  high  object.     It 
happens  sometimes  that  the  negative  charge  is  induced  in  a 
neighboring  cloud,  and  then  we  see  a  beautiful  display  of 
lightning  between  the  two  oppositely  charged  clouds,  and  no 
damage  is  done  by  the  discharge. 

During  the  hot  weather  of  summer  there  are  few  nights  in  which 
one  cannot  observe  the  reflection,  from  clouds  near  the  horizon  or 
from  the  air,  of  flashes  of  lightning  in  a  distant  storm.  The  storm 
may  be  fifty  miles  away  and  entirely  below  the  horizon.  This  form 
is  often  erroneously  called  heat  lightning. 

374.  Thunder.  —  In  the  case  of  a  lightning  flash  the  air 
is  the  dielectric  which  is  broken  through,  and  since  the 
velocity  of  the  discharge  is  very  great,  it  is  probable  that  a 
compression  wave  is  set  up  in  the  air  like  that  which  is 
set  up  by  a  flying  cannon  ball  and  that  this  wave  striking 
the  ear  produces  the  sound  of  the  thunder.     Other  causes 
may  help  to  produce  it,  such  as  the  restoring  to  a  con- 
dition of  rest  of  the  air  that  has  been  broken  through  by 
the   flash,    or   the  formation  of   steam  from  the  moisture 
in  the  air,   caused   by    the    heat    of    the    discharge.    To 
a   person   who   is   near   the   flash   the  sound   is  that  of  a 
crash,  but  to  one  at   some  distance  the  direct  report  is 


344  ELECTRICITY 

mingled  with  its  echo  from  the  clouds  and  the  earth,  pro- 
ducing the  deep,  rolling  sound  that  we  call  thunder. 

375.  Lightning  Rods.  —  Franklin's  invention  of  the  light- 
ning rod  was  the  natural  outcome  of  his  experiment  with 
the  kite.     The  function  of  the  lightning  rod  is  not  to  attract 
a  stroke  of  lightning,  but  to  reduce  the  potential  difference 
between  the  clouds  and  the  earth  by  a  quiet  discharge.     To 
secure  this,  the  rod  must  be  well  supplied  with  points  at 
the  top  and  must  make  a  permanent  connection  with  the 
damp  earth  below.     Copper  sheets  fastened  to  the  lower 
end  of  the  rod  make  a  good  earth  connection.     If  a  full 
lightning  discharge  from  the  clouds  to  the  earth  should  strike 
a  lightning  rod,  the  building  might  be  damaged,  just  as  Dr. 
Franklin  might  have  been  killed  had  lightning  struck  his 
kite. 

376.  The  Aurora  Borealis  and  Northern  Lights  are  names 
given  to  beautiful  light  phenomena  in  the  northern  part  of 
the  northern  hemisphere.     The  general  explanation  is  that 
the  aurora  is  an  electrical  discharge  taking  place  in  the  upper 
regions  of  the  air,  where  its  density  is  much  less  than  at  the 
surface  of  the  earth.     The  position  of  the  aurora  and  the 
direction  of  its  streamers  seem  to  be  definitely  connected 
with   the  magnetic  condition  of  the  earth,   the  streamers 
centering  at  the  north  magnetic  pole,  as  reported  by  Arctic 
explorers. 

Questions 

1.  In  sharpening  a  pencil,  the  shavings  sometimes  cling  to  the 
knife  or  the  pencil.     Why  ? 

2.  How  would  you  determine  the  kind  of  electricity  with  which 
a  body  is  charged? 


STATIC   ELECTRICITY  345 

3.  Why  does  a  charge  go  to  the  outside  of  an  insulated  tin  can? 

4.  What  will  be  the  force  and  character  of  the  mutual  action 
between  a  -f-  charge  of  10  units  and  a  —  charge  of  6  units,  if  the  two 
are  2  cm.  apart?     What  between  a  —  charge  of  20  units  and  a  — 
charge  of  10  units  3  cm.  apart? 

5.  If  one  end  of  a  wooden  stick  that  is  supported  on  a  glass 
stand  is  brought  near  the  knob  of  an  electroscope,  and  a  charged 
glass  rod  is  brought  near  the  other  end  of  the  stick,  the  leaves  will 
gradually  separate.     Why? 

6.  Figure    321    shows    a 
glass  tube  with  a  wire  wound 
spirally    around  it  from  one 

end  to  within  three  inches  of  the  other.  If 
the  unwound  end  of  the  tube  is  heated  red- 
hot,  and  the  tube  and  wire  are  then  held  in 
the  hand  by  the  other  end,  while  the  hot  end 
is  held  to  the  knob  of  a  charged  electroscope, 

the  leaves  will  go  together.     What  does  this 

9  FIG.  321 

prove  ' 

7.  What  would  be  the  effect  of  running  a  metal  pin,  connected 
with  the  earth,  through  the  glass  plate  of  an  electrophorus,  until  it 

^_  almost  or  quite  touches  the  disk  when  it  is  resting 

,     on  the  glass?     Explain. 

8.  Explain  why  the  electric  whirl  shown  in  Fig. 
322  will  rotate  when  put  in  contact  with  one  side  of 
an  electric  machine.     Does  it  make  any  difference 
whether  the  whirl  is  connected  with  the  +  side  of 

FIG.  322         the  machine  or  with  the  —  side  ?    Explain. 

9.  Why  is  the  spark  thicker  when  Leyden  jars 
are  used  with  the  machine  than  when  they  are  not  ? 

10.  What  are  the  essentials  of  a  condenser?    What  might  result 
from  making  a  Leyden  jar  from  a  very  thin  beaker? 

11.  Can  you  charge  a  Leyden  jar  heavily  if  it  stands  on  a  glass 
plate?    Why? 

12.  A  pith  ball  is  placed  upon  a  metal  plate  connected  with  the 
earth.     A  similar  plate  connected  with  the  positive  pole  of  an  electric 
machine  is  suspended  over  it.    The  pith  ball  rapidly  passes  from  one 
plate  to  the  other.    Explain. 


346 


ELECTRICITY 


Zn, 


II.  CURRENT  ELECTRICITY 

377.  The  Electric  Current.  —  The  discharge  of  electricity 
that  takes  place  when  a  spark  passes  between  the  coatings 
of  a  Leyden  jar  is  an  electric  current.  The  time  during 
which  the  current  passes,  however,  is  very  short.  Con- 
tinuous currents  are  produced  whenever  a  conductor  con- 
nects two  points  at  which  a  difference  of  potential  is  con- 
stantly maintained. 

Demonstrations.  —  Make  a  solution  of  sulphuric  acid  (H2S04) 
by  pouring  slowly  5  c.c.  of  the  acid  into  100  c.c.  of  water.  Place  a 
strip  of  copper  and  a  strip  of  zinc  in  the  jar  containing  the  dilute  acid. 
As  long  as  the  plates  are  separated,  the  only 
action  that  takes  place  is  the  formation  of  a 
few  hydrogen  bubbles  on  the  surface  of  the 
zinc  plate.  But  as  soon  as  the  two  plates  are 
brought  in  contact  —  which  may  be  done  by 
bending  the  plate  as  in  Fig.  323  —  there  is  a 
rapid  giving  off  of  hydrogen  from  the  surface 
of  the  copper  plate. 

Solder  a  copper  wire  to  a  thin  sheet  of  cop- 
per, and  attach  a  binding  post  to  a  zinc  bat- 
tery plate.  Repeat  the  preceding  demonstration  with  these  plates 
and  observe  that  the  change  in  the  formation  of  gas  takes  place  just 
when  the  copper  wire  is  attached  to  the  binding  post  on  the  zinc 
plate.  Disconnect,  bring  the  wire  over  and 
parallel  to  a  magnetic  needle,  and  the  needle 
will  be  deflected  as  soon  as  the  wire  is  again 
touched  to  the  binding  post.  The  needle 
swings  back  to  its  original  position  as  soon 
as  the  wire  is  disconnected,  or  when  either 
plate  is  lifted  out  of  the  solution. 

In  the  last  demonstration  the  deflec- 
tion of  the  needle  is  caused  by  the  pas- 
sage of  an  electric  current.  As  soon  as  PIG.  324 


FIG.  323 


CURRENT  ELECTRICITY  347 

the  plates  are  joined  by  a  wire,  as  in  Fig.  324,  the  current 
passes  in  the  external  circuit  from  the  copper  to  the  zinc, 
while  the  difference  of  potential  is  maintained  by  continued 
chemical  action  in  the  cell. 

378.  The  Poles  of  a  Cell.  —  The  apparatus  just  described 
constitutes  a  voltaic  cell,  or  galvanic  cell.     The  terminals 
of  the  plates  to  which  the  conductor  is  attached  are  called 
the  poles  of  the  cell,  the  zinc  being  the  negative  and  the 
copper  the  positive  pole.     When  the  poles  are  joined  by  a 
conductor,  the  cell  is  on  a  closed  circuit;  when  they  are  not, 
it  is  on  an  open  circuit. 

379.  Chemical  Action  in  the  Cell.  —  The  phenomena  tak- 
ing place  in  the  cell  are  practically  as  follows :  When  the 
zinc  goes  into  solution  with  the  H2SO4,  it  does  so  in  the 
form  of  ions,  i.e.,  atoms  or  groups  of  atoms,  charged  with 
positive  electricity.     These  zinc  ions  leave  the  zinc  plate 
negatively  charged  by  the  separation,  and  displace  positive 
hydrogen  ions  in  the  solution  H2SO4,  forming  zinc  sulphate 
(ZnSO4).     The  positive  ions  of  displaced  hydrogen,  repelled 
by  the  positive  ions  of  zinc  in  the  solution,  move  to  the  copper 
plate,  and,   discharging  their  positive  electricity  upon  it, 
pass  off  in  the  form  of  hydrogen  gas.     Jn  chemical  symbols 
the  action  is  as  follows  : 

Zn  +  H2SO4  =  ZnSO4  +  H2. 

The  migration,  as  it  is  called,  of  positive  H  ions  toward  the 
copper,  and  of  negative  SO4  ions  toward  the  zinc,  depends 
upon  the  dissociation  of  some  of  the  molecules  of  the  H2SO4 
into  hydrogen,  HH,  and  sulphion,  SO4,  in  the  solution. 

If  the  cell  is  on  an  open  circuit,  this  action  diminishes 
as  the  charges  on  the  plates  increase,  and  finally  stops, 


348  ELECTRICITY 

having  produced  a  difference  of  potential  between  the  zinc 
and  copper  plates  that  constitutes  the  electro-motive  force  of 
the  cell. 

The  action  stops  when  the  attraction  of  —  S04  ions  for  +  zinc 
ions  is  counterbalanced  by  the  attraction  of  the  —  zinc  plate  for  the 
4-  zinc  ions ;  and  when  the  repulsion  of  the  +  zinc  ions  against  the 
+  hydrogen  ions  is  counterbalanced  by  that  of  the  +  copper  plate. 
If  the  cell  is  on  a  closed  circuit,  the  positive  charge  on  the  copper 
plate  discharges  through  the  circuit  and  neutralizes  the  negative 
charge  on  the  zinc  plate,  producing  'an  electric  current,  and  the 
action  is  continuous. 

380.  Local  Action ;   Amalgamating  the   Zinc.  —  When  a 
strip  of  zinc  is  placed  in  the  acid,  hydrogen  bubbles  are  given 
off  from  its  surface.     This  is  due  to  the  setting  up  of  an  elec- 
tric current  between  impurities  in  the  zinc  and  the  zinc 
itself  through  the  acid  and  is  called  local  action.     The  exist- 
ence of  these  impurities  can  be  proved  by  leaving  the  zinc 
in  the  acid  for  five  minutes,  when  it  will  be  found  covered 
with  a  black  deposit  that  can  be  wiped  off. 

If  a  particle  of  carbon  is  at  A  (Fig.  325),  a  local  current 
will  be  set  up  between  it  and  the  zinc,  and  as  a  result  hydrogen 
will  be  set  free.     In  order  to  prevent  this  action, 
which  reduces  the  surface  of  the  plate  for  the 
main  current,  the  zinc  is  cleaned  by  dipping  it  in 
dilute  sulphuric  acid  and  then  rubbing  with  mer- 
cury.    This  has  the  property  of  dissolving  the 
FIG.  325       .    '        ,  p  .,  , .  f        - 

zinc  and  forming  a  covering  over  the  particles  or 

carbon  as  shown  at  B  in  Fig.  325,  thus  preventing  the  car- 
bon from  coming  in  contact  with  the  acid. 

381.  Polarization  of  the  Cell.  —  When  the  circuit  is  made 
in  the  simple  voltaic  cell,  it  is  noticed  that,  while  bubbles 
of  hydrogen  rise  to  the  surface  of  the  liquid,  the  copper 


CURRENT  ELECTRICITY  349 

plate  is  kept  pretty  nearly  covered  by  them  all  the  time. 
This  causes  what  is  known  as  polarization  of  the  cell  and  has 
two  eft'ects :  (1)  it  reduces  the  amount  of  surface  of  the 
plate  exposed  to  the  liquid,  and  (2)  it  reduces  the  difference 
of  potential  between  the  plates.  Both  of  these  results  tend 
to  lessen  the  amount  of  current  that  can  be  sent  by  the  cell. 
The  usual  way  in  which  this  difficulty  is  overcome  is  by  the 
use  of  a  kind  of  liquid  that  will  oxidize  the  hydrogen  before 
it  is  deposited  on  the  plate. 

\  382.  Different  Forms  of  Cells.  —  Many  different  sub- 
stances may  be  used  in  place  of  the  copper,  zinc,  and  sul- 
phuric acid  in  the  simple  cell  described  above.  It  is  always 
necessary,  however,  that  the  acid  or  salt  in  the  solution  shall 
act  more  strongly  on  one  of  the  plates  than  on  the  other. 
There  are  many  different  forms  of  cells  in  use,  but  most  of 
them  have  zinc  as  the  metal  to  be  acted  upon.  These  may 
be  grouped  in  classes,  of  which  the  following  are  types. 

383.  The  Daniell  Cell.  —  This  is  an  early  form  of  cell  in 
which  a  zinc  bar  is  placed  in  a  porous  cup  containing  dilute 
sulphuric  acid,  while  a  copper  cylin- 
der arid  a  solution  of  copper  sulphate 
are  in  a  larger  glass  jar  holding  the 
porous  cup.  As  the  sulphuric  acid 
acts  upon  the  zinc,  zinc  sulphate  is 
formed  within  the  porous  cup,  while 
hydrogen  is  displaced  from  the  sul- 
phuric acid  and  passes  through  the 
porous  cup.  This  hydrogen  displaces 
the  copper  from  the  copper  sulphate  FlG-  326 

and  the  copper  is  deposited  on  the  copper  plate.  In  order 
to  keep  up  the  strength  of  the  copper  sulphate  solution, 


350 


ELECTRICITY 


copper  sulphate  crystals  are  placed  in  a  cup  attached  to  the 
cylinder  in  the  outer  jar. 

384.  The  Gravity  Cell.  —  In  the  crowfoot  type  of  gravity 
cell  a  star-shaped  group  of  copper  sheets,  surrounded  by 

crystals  of  copper  sulphate 
(CuS04),  is  placed  in  the  bottom 
of  a  glass  jar.  Water  to  which 
a  few  drops  of  sulphuric  acid 
have  been  added  is  poured  in 
until  the  cell  is  nearly  full,  and 
then  a  zinc  plate  or  "  crowfoot  " 
is  hung  from  the  upper  edge  of 
the  jar. 

As    the    sulphuric    acid    acts 

upon  the  zinc,  zinc  sulphate  is 
FIG.  327.  — Crowfoot  Gravity  Cell    „  ,      ,,  .      .     ,  , 

formed ;  this  is  less  dense  than 

copper  sulphate,  and  they  keep  separate  in  the  gravity  cell 
without  the  porous  cup. 

Since  polarization  does  not  take  place  in  the  gravity  cell, 
it  maintains  a  practically  constant  difference  of  potential 
at  its  terminals,  and  is  capable  of  giving  a  nearly  constant 
current.  This  is  the  cell  ordinarily  used  for  telegraphic  work. 

When  this  cell  is  in  good  condition,  the  blue  solution  of 
copper  sulphate  should  fill  the  jar  to  a  little  above  the  middle, 
and  the  line  of  separation  between  it  and  the  zinc  sulphate 
solution  should  be  clearly  defined.  If  the  cell  is  unused  for 
some  time,  the  copper  sulphate  solution  will  reach  the  zinc, 
and  copper  will  be  deposited  upon  it.  The  cell  can  be 
brought  back  to  its  proper  condition  by  short-circuiting  it, 
that  is,  connecting  the  two  terminals  by  a  short  piece  of  wire, 
for  a  few  hours. 


CURRENT  ELECTRICITY 


351 


As  the  water  evaporates,  the  zinc  sulphate  crystallizes 
in  the  form  of  white  crystals  around  the  edge  of  the  jar,  and 
unless  this  is  coated 
with  paraffin,  the  crys- 
tals will  form  over  the 
top  and  down  the  out- 
side of  the  jar. 


FIG.  328 


385.  The  Leclanche 
Cell  has  in  the  center 
a  porous  cup  contain- 
ing a  bar  of  carbon, 
around  which  is  packed 
a  mixture  of  manganese  dioxide  and  coke.  The  top  of  the 
porous  cup  is  sealed  to  keep  the  contents  in  place.  The 
carbon  is  the  positive  pole  and  a 
rod  of  zinc  at  the  side  of  the  jar  is 
the  negative.  The  liquid  used  is 
a  solution  of  ammonium  chloride 
(sal  ammoniac).  This  cell  polarizes 
rapidly  and  is  suitable  for  open 
circuit  work  only.  It  is  largely  used 
for  electric  bells.  It  needs  but  little 
attention  after  it  is  once  properly 
charged.  A  modification  of  this  cell 
is  shown  in  Fig.  328. 

386.  The    Bichromate    Cell. —  In 
the  bichromate  cell  and  the  chromic 
FIG.  329.— Bichromate      acid  cell  the   chemical  action  upon 
the  zinc  goes  on  vigorously  whether 

the  circuit  is  open  or  closed,  and  for  this  reason  the  zinc  is 
so  arranged  that  it  can  be  raised  out  of  the  liquid  when  the 


352 


ELECTRICITY 


current  is  not  needed.  A  common  form  is  that  known  as 
the  bottle  form,  shown  in  Fig.  329.  Two  plates  of  carbon 
are  suspended  from  the  top  of  the  bottle,  while  between 
them  is  a  rod  carrying  at  its  lower  end  a  zinc  plate  that  can 
be  raised  and  lowered  at  will. 

The  solution  used  may  be  either  potassium  bichromate  or 
chromic  acid,  but  the  latter  is  the  more  convenient  to  make. 

Chromic  Add  Solution.  — •  Dissolve  160  g.  of  chromic  acid  in 
1420  c.c.  of  water,  and  add  slowly,  stirring  all  the  while,  90  c.c.  of 
sulphuric  acid. 

387.  The  Dry  Cell  is  hermetically  sealed  at  the  top  so  that 
its   contents   cannot  escape.     The   containing   cup,   Zn  in 

Fig.  330,  is  of  zinc,  and  one  terminal 
of  the  cell  is  attached  to  it.  The 
other  terminal  is  at  the  top  of  a  cylin- 
der or  plate  C,  composed  of  carbon 
and  manganese  dioxide.  The  space 
between  this  and  the  zinc  cup  is  filled 
with  a  paste  composed  of  one  part  by 
weight  of  zinc  oxide,  one  part  zinc 
chloride,  one  part  ammonium  chloride, 
three  parts  plaster  of  Paris,  and  two 
parts  water.  This  is  an  open-circuit 
cell.  It  polarizes  rather  quickly,  but 
is  rapidly  restored  to  its  initial  con- 
dition on  breaking  the  circuit.  This 
form  of  cell  is  sometimes  used  to  furnish  the  spark  for  ex- 
ploding the  gas  in  automobile  engines. 

388.  Electro-motive   Force,    Current,    Resistance.  —  The 

difference  of  potential  at  the  terminals  of  a  cell  when  it  is  on 
open  circuit  is  its  electro-motive  force,  or  E.  M.  F.  When  the 
cell  is  sending  a  current,  the  difference  of  potential  at  its 


FIG.  330.  — Dry  Cell 


CURRENT  ELECTRICITY  353 

terminals  is  less,  —  by  an  amount  called  the  loss  of  potential 
in  the  cell.  In  Fig.  331  the  cell  with  terminals  A  and  D  is 
sending  a  current  through  the 
circuit  from  A  to  B,  C,  D,  and 
back  to  A.  The  sum  of  the 
differences  of  potential  be- 
tween A  and  B,  B  and  C,  and 
C  and  D,  is  equal  to  the  dif- 
ference of  potential  between 

FIG.  331 

A  and  D ;   and  if  to  this  we 

add  the  loss  of  potential  in  the  cell,  the  sum  is  equal  to 
the  E.  M.  F.  of  the  cell.  The  practical  unit  of  E.  M.  F.  and 
also  of  potential  difference,  is  the  volt. 

When  the  two  poles  of  a  cell  are  connected  by  a  conductor, 
as  in  Fig.  331,  a  current  is  said  to  flow  from  the  +  to  the  — . 
The  practical  unit  of  current  is  the  ampere. 

If  we  connect  the  poles  of  the  cell  by  a  short,  heavy  wire, 
and  measure  the  current  that  passes,  and  if  we  then  connect 
the  poles  with  a  long,  thin  wire,  and  again  measure  the 
current,  we  find  that  the  -greater  current  is  passing  in  the  first 
case.  We  see,  therefore,  that  the  wire  has  a  certain  property 
that  affects  the  amount  of  current  passing  through  it.  This 
property  is  called  resistance,  the  unit  of  which  is  the  ohm. 

The  current  of  electricity  passing  along  a  wire  is  some- 
what analogous  to  the  flow  of  water  in  a  pipe.  The  current 
or  amount  of  water  that  flows  through  a  pipe  depends  upon 
two  things :  (1)  the  difference  between  the  water  levels  at 
the  ends  of  the  pipe,  or  the  "  head  "  of  water ;  and  (2)  the 
size  and  smoothness  of  the  inside  of  the  pipe.  The  "  head  " 
or  difference  of  water  pressure  at  the  two  ends  of  the  water 
pipe  may  be  compared  to  the  difference  of  potential,  or  differ- 
ence of  electrical  pressure,  at  the  ends  of  a  wire ;  the  resist- 

Rev. 


354  ELECTRICITY 

ance  to  the  flow  of  water  in  the  pipe,  depending  on  size  and 
roughness,  may  be  compared  to  the  resistance  to  the  electrical 
current,  depending  on  the  cross  section  and  material  of  a  wire ; 
and  the  resulting  current  of  water  may  be  compared  to  the 
electrical  current. 

389.  The  Unit  of  Current,  the  Ampere.  —  The  chemical, 
the  magnetic,  or  the  heating  effect  may  be  taken  as  a  basis 
for  measurement  of  currents.     The  chemical  effect,  however, 
is  taken  to  define  the  unit,  and  the  magnetic  effect  for  practi- 
cal use. 

The  ampere  is  that  current  that  will  deposit  0.001118  g. 
(0.01725  grain)  of  silver  per  second  from  a  solution  of  silver 
nitrate.  The  same  current  will  deposit  0.00032959  g. 
(0.005086  grain)  of  copper  per  second  from  a  solution  of  cop- 
per sulphate  (§  421). 

For  the  measurement  of  small  currents  the  milliampere,  or  thou- 
sandth part  of  an  ampere,  is  used  as  a  unit. 

390.  The  Unit  of  Resistance.  —  The  ohm  is  defined  as  the 
resistance  of  a   column  of   mercury  the  mass  of   which  is 
14.4521  g.  and  which  has  a  uniform  cross  section,  and  a 
length  of  106.3  ±  cm.  at  0°  C.     This  is  practically  a  column 
106.3  cm.  long  and  1  sq.  mm.  in  cross  section.     Ten  feet  of 
No.  30  copper  wire  has  a  resistance  of  1.033  ohms. 

A  megohm  is  a  million  ohms.  A  microhm  is  one  millionth  of  an 
ohm. 

391.  The  Laws  of  Resistance.  —  The  resistance  of  a  con- 
ductor depends  upon  four  things :  length,  cross  section,  ma- 
terial,  and   temperature.     Experiment  has   determined  the 
following  laws : 

I.  The  resistance  of  a  conductor  is  directly  proportional 
to  its  length. 


CURRENT  ELECTRICITY 


355 


II.  The  resistance  of  a  conductor  is  inversely  proportional 
to  its  area  of  cross  section.     For  a  wire  a  more  convenient 
form  of  the  law  is  that  the  resistance  is  inversely  propor- 
tional to  the  square  of  the  diameter  of  the  wire. 

III.  The  resistance  of  a  conductor  depends  upon  its  material. 

IV.  The  resistance  of  a  metallic  conductor  increases  as  its 
temperature  rises.     The  resistance  of  carbon  and  electrolytes, 
on  the  other  hand,  decreases. 

The  first  three  laws,  for  a  wire,  may  be  expressed  by  the 

formula  T.  I 

R  =  K-,  (53) 

in  which  I  is  the  length  in  feet,  d  the  diameter  in  thousandths 
of  an  inch,  or  mils,  and  K  is  the  resistance  of  1  mil  foot  of 
the  wire ;  i.e.,  of  a  wire  1  foot  long  and  1  mil  in  diameter. 

VALUES  OF  K  AT  75°  F. 

.      9.76  Platinum  .     .      58.80 

.     10.38  Iron      .     .     .       63.08 

.     19.00  German  silver     135.92 

COPPER  WIRE  TABLE 
Temperature  =  75°F.     Sp.  gr.  =  8.89 


Silver  .  . 
Copper  . 
Aluminum 


No. 

DlAM. 

IN  MILS 

OHMS  PEB 
1000  FEET 

FEET  PER 
POUND 

No. 

DlAM. 

IN  MILS 

OHMS  PER 
1000  FEET 

FEET  PER 
POUND 

1 

289.3 

0.124 

3.95 

16 

50.82 

4.02 

128.14 

2 

257.6 

0.156 

4.99 

17 

45.26 

5.07 

161.59 

3 

229.4 

0.197 

6.29 

18 

40.30 

6.39 

203.76 

4 

204.3 

0.249 

'     7.93 

19 

35.39 

8.29 

264.26 

5 

181.9 

0.314 

10.00 

20 

31.96 

10.16 

324.00 

6 

162.0 

0.395 

12.61 

21 

28.46 

12.82 

408.56 

7 

144.3 

0.499 

15.90 

22 

25.35 

16.15 

515.15 

8 

128.5 

0.629 

20.05 

23 

22.57 

20.38 

649.66 

9 

114.4 

0.793 

25.28 

24 

20.10 

25.70  • 

>   819.21 

10 

101.9 

1.00 

31.38 

25 

17.90 

32.40 

1032.96 

11 

90.74 

1.26 

40.20 

26 

15.94 

40.47 

1302.61 

12 

80.81 

1.59 

50.69 

27 

14.20 

51.52 

1642.55 

13 

71.96 

2.00 

63.91 

28 

12.64 

64.97 

2071.22 

14 

64.08 

2.59 

80.59 

29 

11.26 

81.92 

2611.82 

15 

57.07 

3.12 

101.63 

30 

10.03 

103.30 

3293.97 

356 


ELECTRICITY 


It  is  well  to  notice  certain  facts  concerning  the  above  table 
as  follows :  The  diameter  of  wire  for  a  certain  number  is  one 
half  as  great  as  it  is  for  the  sixth  number  before  it.  The  re- 
sistance and  the  number  of  feet  per  pound  doubles  every 
third  number.  If  one  remembers,  for  example,  that  copper 
wire  No.  10  is  practically  100  mils  in  diameter,  has  a  resistance 
of  1  ohm  per  thousand  feet,  and  contains  31.4  feet  per  pound, 
he  can  make  a  very  good  estimate  for  wire  of  any  length  and 
size. 


392.  Unit  of  Electromotive  Force,  the  Volt.  —  The  volt 
is  the  difference  of  potential  required  at  the  ends  of  a  con- 
ductor, the  resistance  of  which  is  1  ohm,  to  send  through  it 
a  current  of  1  ampere. 

The  E.  M.  F.  of  a  cell  depends  only  upon  the  materials 
of  which  it  is  composed,  and  not  at  all  upon  its  size  or  shape. 
The  gravity  cell  gives  nearly  1.1  volts;  the  Leclanche  cell, 
about  1.5  volts;  and  the  chromic  acid  cell,  about  2  volts. 
Many  attempts  have  been  made  to  produce  a  standard  cell. 
In  such  a  cell  it  is  not  at  all  essential  that  the  E.  M.  F. 

should  be  1,  but  the  E. 
M.  F.,  whatever  it  is, 
should  remain  constant. 
The  legal  standard  cell  in 
the  United  States  is  the 
Clark  cell.  Its  E.  M.  F. 
1.434  volts  at  15°  C. 


CADMIUM 

SULPHATE 

CRYSTALS 

AND  SOLUTION. 


MERCUROU9 
SULPHATE  PASTE. 

PLATINUM  WIRE. 
MERCURY. 


s 


FIG.  332. — Weston  Standard  Cell 


The  Weston  or  cadmium 
standard  cell  has  an  E. 
M.  F.  of  1.0186  volts  between  5°  C.  and  26°  C.  The  stand- 
ard cell  is  not  used  for  the  production  of  a  current  but  for 
comparing  its  voltage  with  that  of  other  cells. 


CURRENT  ELECTRICITY  357 

393.  Ohm's  Law,  formulated  as  the  result  of  experiment, 
is  of  very  great  importance.     It  is  to  the  effect  that  the 
current  varies  directly  as  the  electro-motive  force  and  in- 
versely as  the  resistance,  and  that  their  relation  is  expressed 
by  the  formula  T? 

;.'    .  ••.: '"*•  (54) 

This  may  be  written 

A  Volts  F 

Amperes  =  — ,  or  A  =  — . 

Ohms  0 

From  this  law  we  can  find  the  current  that  a  known  E.  M.  F. 
will  send  through  a  certain  resistance,  the  resistance  through 
which  a  known  E.  M.  F.  will  send  a  given  current,  or  the 
E.  M.  F.  required  to  send  a  certain  current  through  a  known 
resistance.  The  law  may  also  be  applied  to  difference  of 
potential  instead  of  to  E.  M.  F. 

394.  Size  and  E.  M.  F.  of  a  Cell.  — Demonstration.  —  Couple 
the  plates  of  a  simple  galvanic  cell  to  a  voltmeter,  and  note  the  read- 
ing.    Diminish  the  distance  between  the  plates  and  then  lift  one 
plate  slowly  until  it  is  nearly  out  of  the  liquid.     Observe  that  the 
reading  of  the  voltmeter  is  not  changed. 

The  size  of  a  cell  makes  no  difference  in  its  E.  M.  F. 

395.  Internal  Resistance  of  a  Cell. — Demonstration.  —  Con- 
nect the  cell  used  in  §  394  to  an  ammeter,  and  observe  that  the 
current  increases  when  the  distance  between  the  plates  is  decreased, 
and  decreases  while  the  plate  is  being  lifted  from  the  liquid. 

Since  the  E.  M.  F.  of  the  cell  remains  constant,  this  change 
in  the  current  must  be  due  to  a  change  in  the  resistance  of 
the  cell.  The  resistance  of  a  cell-  is  called  internal  resistance 
and  depends  upon  the  size,  shape,  and  material  of  the  cell. 
It  is  this  internal  resistance  that  causes  the  loss  of  potential 
in  the  cell  (§  388). 


358  ELECTRICITY 

396.  Arrangement  of  Cells  in  a  Battery  ;  Series  Grouping. 
—  Whenever  several  cells  are  to  be  grouped  in  a  battery, 
the  question  of  how  they  shall  be  coupled  together  becomes 
an  important  one.  As  horses  can  be  hitched  to  a  wagon, 
either  one  behind  the  other  (tandem)  or  side  by  side  (abreast) 
so  cells  can  be  coupled  either  in  series  or  in  parallel.  When 

B  two  or  more  cells  are 
coupled  in  series,  the 
copper  of  one  is  joined 
to  the  zinc  of  the  next, 
while  the  outside  cop- 

per  and  zinc  form  the  terminals  of  the  battery,  as  A  and  B  in 
Fig.  333.  For  this  grouping  the  E.  M.  F.  of  one  cell  is 
added  to  that  of  the  next,  and  the  total  internal  resistance 
is  the  sum  of  the  internal  resistances  of  all  the  cells  ;  hence 
Ohm's  Law  will  be  written 

f='  (55) 


in  which  S  is  the  number  of  cells  in  series  ;  E,  the  E.  M.  F. 
of  each  cell  ;  b,  the  internal  resistance  of  each  cell  ;  and  R, 
the  resistances  of  all  conductors  and  instruments  through 
which  the  current  passes. 

EXAMPLE.  —  Suppose  4  cells  to  be  coupled  in  series,  the  E.  M.  F. 
of  each  to  be  1.02  volts,  and  the  internal  resistance  of  each  2.4  ohms, 
what  current  will  they  send  through  an  external  resistance  of  27 
ohms? 

7,_gJL._      4X1.02      =^=0.lllampere. 
Sb  +  R      4  X  2.4  +  27      36.6 

397.  Parallel  Grouping.  —  In  the  parallel  or  multiple 
method  of  grouping,  the  coppers  are  all  joined  to  one  ter- 
minal and  the  zincs  to  another.  This  gives  the  same  result 


CURRENT  ELECTRICITY 


359 


as  if  all  the  plates  were  in  one  large  cell.     The  E.  M.  F.  is 
the  same  as  it  would  be  for  a  single  cell,  while  the  internal 
resistance  is  less.     Ohm's  Law  will  be : 
E 


7  = 


(56) 


FIG.  334.  —  In  Parallel 


in  which  P  is  the  number 
of  cells  in  parallel. 

EXAMPLE.  —  Suppose  the  same  4  cells  as  in  §  396  to  be  grouped 
in  parallel  and  to  be  coupled  to  the  same  resistance.     What  will  be 

the  current? 

E              1.02  1.02       .__,_ 

I  =  -r =  — =  i^r^  =  0.037  ampere. 

0      ,       7-1  ^.4        ,      r»T  Z/.O 


398.  The  Series  and  Parallel  Grouping  is  a  combination 
of  the  two  methods  given  above.  In  Fig.  335  there  are  6  cells 
arranged  3  in  series  and  2  in  parallel.  In  Fig.  336  the  same 


FIG.  335 


FIG.  336 


6  cells  are  coupled  2  in  series  and  3  in  parallel.  In  each  case 
the  total  number  of  cells  is  the  product  of  the  number  in  series 
and  the  number  in  'parallel.  Ohm's  Law  applied  to  this 
coupling  is :  SE 

=  Sb  +  R  (57) 

P 


360  ELECTRICITY 

in  which  each  letter  has  the  same  meaning  as  in  §§  396, 
397. 

EXAMPLE.  —  If  the  cells  in  Fig.  336  are  of  the  same  kind  as  those 
used  in  §  396,  with  the  same  external  resistance,  then 

8E             2  X  1.02          2.04 
I  =  ™ =  r»  v  9  A =  ofic  =  °-071  ampere. 

oo        p       2  X  ZA    .   07       28.O 

P   "  3 

The  formulas  given  for  these  different  groupings  are  im- 
portant, and  are  applicable  to  any  form  of  continuous  current 
generators,  dynamos  as  well  as  cells. 

399.  Arrangement  of   Cells  for  Maximum  Current.  —  In 
order  to  get  the  maximum  current  from  a  battery,,  the  cells 
should  be  grouped  in  such  a  way  that  their  internal  resist- 
ance shall  be  as  near  as  possible  the  same  as  the  external 
resistance  of  the  circuit.     This  means  that  if  R  is  large, 
the  cells  should  be  grouped  in  series;  if  it  is  small,  they 
should  be  in  parallel;  and  if  it  is  neither  very  large  nor 
very  small,  such  a  grouping  should  be  made  as  will  make 

^  =  R,  if  possible. 

400.  Maximum  Efficiency.  —  The  arrangement  for  maxi- 
mum current  is  not  usually  the  one  for  maximum  efficiency ; 
for,  if  the  internal  resistance  is  equal  to  the  external,  just 
half  the  work  of  the  current  is  spent  in  overcoming  resist- 
ance in  the  cells ;  that  is,  the  efficiency  is  just  50  per  cent. 
The  efficiency  will  increase  if  the  external  resistance  is  made 
large  compared  with  the  internal,  for  now  the  greater  part 
of  the  work  will  be  employed  outside  the  cell.     This  means 
that  a  cell  cannot  work  efficiently  when  sending  a  heavy 
current. 


CURRENT  ELECTRICITY  361 

Questions 

1.  How  does  the  current  given  by  a  cell  differ  from  that  given 
by  the  Holtz  machine  ? 

2.  Why  is  it  not  necessary  to  use  a  porous  jar  in  the  gravity 
cell? 

3.  Will  the  current  from  a  cell  jump  across  a  small  air  gap  in  the 
same  way  that  the  spark  will  jump  from  a  Leyden  jar? 

4.  Why  will  a  light  cotton  covering  insulate  a  current  for  an 
electric  light,  while  it  will  not  for  the  current  from  an  induction 
machine  ? 

5.  Which  will  have  the  greater  resistance,  a  spool  wound  full  of 
small  wire  or  a  spool  of  the  same  size  wound  full  of  large  wire? 
Give  two  reasons. 

6.  What  is  meant  by  a  mil  foot  ? 

7.  What  effect  will  it  have  upon  the  internal  resistance  of  a 
cell  to  move  the  positive  and  negative  plates  nearer  together? 

8.  What  effect  will  it  have  to  increase  the  size  of  the  plates? 

9.  Is  it  an  economical  use  of  a  battery  to  couple  the  cells  in  such 
a  manner  as  to  get  the  maximum  current  ? 

10.  What  effect  will  it  have  upon  the  rate  of  work  done  by  a 
battery  if  it  is  used  at  high  efficiency? 

Problems 

1.  What  is  the  resistance  of  2640  ft.  of  copper  wire  No.  18? 

2.  What  is  the  resistance  of  iron  wire  having  the  same  length 
and  diameter? 

3.  What  is  the  resistance  of  100  ft.  of  German  silver  wire  No. 
30? 

4.  A  Daniell  cell,  having  an  E.  M.  F.  of  1.06  volts,  and  an  in- 
ternal resistance  of  0.4  ohm,  is  coupled  to  a  coil  of  wire  having  a 
resistance  of  0.38  ohm.     What  current  will  pass  through  ? 

6.  Four  Daniell  cells  (E.  M.  F.  =  1.06  volts,  and  an  internal 
resistance  of  0.4  ohm)  are  coupled  in  series  and  send  a  current 
through  a  resistance  of  2  ohms.  What  is  the  value  of  the  current 
in  amperes? 

6.  What  current  will  the  same  cells  coupled  in  parallel  send 
through  the  same  resistance? 


362  ELECTRICITY 

7.  A  gravity  cell  of  1.07  volts,  with  an  internal  resistance  of  2.6 
ohms,  is  coupled  to  an  electric  bell  and  push  button.    What  will  be 
the  current  if  the  resistance  of  the  bell  with  the  connecting  wires 
is  5.8  ohms? 

8.  What  will  be  the  current  if  two  cells  like  that  in  problem  7 
are  coupled  in  series  on  that  circuit? 

9.  Find  the  current  if  the  two  cells  are  coupled  in  parallel. 

10.  Six  cells  each  having  an  E.M.F.  of  1.5  volts  and  an  internal 
resistance  of  1.2  ohms  send  a  current  through  a  resistance  of  0.8 
ohm.     How  must  they  be  coupled  to  send  the  maximum  current? 
How  many  amperes  in  this  current? 

11.  How  should  the  cells  of  problem  10  be  coupled  to  send  the 
maximum  current  through  a  resistance  of  8  ohms?     How  many 
amperes  in  this  current? 

12.  Find  the  external  resistance  when  2  dry  cells,  each  having  an 
E.M.F.  of  1.5  volts  and  an  internal  resistance  of  0.6  ohm,  are  coupled 
in  series  and  send  a  current  of  2  amperes  through  it. 


III.    THE  EFFECTS  OF  THE  CURRENT 

401.  Heating  Effects.  —  Demonstrations.  —  Connect    two   dry 
cells  in  series  with  a  short  piece  of  German  silver  wire  No.  30;  the 
wire  will  become  red-hot  unless  you  have  too  long  a  piece.     Use  the 
same  length  of  No.  30  copper  wire  and  repeat.     Can  you  explain  the 
reason  for  any  difference  in  result?     Repeat,  using  a  heavy  current. 

402.  The  Laws  of  Electric  Heating.  —  The  heat  developed 
by  a  current  in  a  circuit  is  proportional  (a)  to  the  square 
of  the  current,  (b)  to  the  resistance  of  the  circuit,1  (c)  to  the 
time  during  which  the  current  passes.     Hence, 

H  =  mPRt, 

in  which  I  represents- the  current  in  amperes,  R  the  resist- 
ance in  ohms,  t  the  time  in  seconds,  and  m  a  constant  factor 


The  resistance  of  German  silver  is  higher  than  that  of  copper. 


THE  EFFECTS  OF  THE  CURRENT 


363 


FIG.  337.  —  Base  of  Electric 
Heater,  partly  cut  away 


'depending  on  the  kind  of  heat  units  in  which  it  is  desired 
to  express  H.    If  H  is  to  be  calories, 

H  =  0.24  PRt.          (58) 

This  heating  effect  is  a  waste  in 
many  uses  of  the  current,  such  as 
in  the  conducting  wires  of  a  street 
railway,  or  of  a  system  of  electric 
lighting.  It  is  called  the  heat  loss 
and  reduces  the  efficiency  of  the 
system.  It  is  made  use  of,  how- 
ever, in  electric  heating,  such  as  the  heating  of  cars,  in  which 
the  current  passes  through  coils  of  resistance  wire,  and  in 
cooking  utensils,  water  heaters,  toasters,  flatirons,  soldering 
irons,  etc. 

403.  Fuse  Wires.  —  Another  useful  purpose  to  which  the 
heating  effect  is  put  is  in  fuse  wires,  which  are  made  of  some 
r^x^     high-resistance  alloy  having  a  low 
melting  point.     If  a  short  piece  of 
such  a  wire  is  put  into  an  electric 

melt   if    ^    current 


FIG.  338.  -Fuse  Link 

increases  beyond  its  carrying  capacity,  and  break  the  circuit. 

In  this  way  a  circuit 

designed   to  carry  a 

certain  current   may 

be  protected  from  an 

accidental    overload. 

Fuses   vary   in  form 

from  the  simple  fuse 

wire  to  the  wire  with  prepared  ends   (Fig.  338)  called  a 

fuse  link,  and  the  cartridge  form  of  inclosed  fuses  that  can 

be  slipped  into  the  terminals  of  the  fuse  block  (Fig.  339)  . 


FIG.  339.  — Cartridge  Fuse 


364 


ELECTRICITY 


FIG.  340 


404.  Magnetic  Effects.  —  Demonstration. — Through  the  mid- 
dle of  a  thick  card  with  a  smooth  surface,  like  bristol  board,  thrust  a 
piece  of  No.  12  copper  wire.  Connect  the 
ends  of  this  wire  with  a  battery  arranged  to 
give  its  maximum  current,  and  while  the 
card  is  supported  in  a  horizontal  position, 
sift  iron  filings  over  it,  and  strike  it  lightly 
with  a  pencil.  If  the  current  is  great 
enough,  the  filings  will  show  that  the  wire 
is  surrounded  by  circular  lines  of  magnetic 
force  having  the  axis  of  the  wire  for  their 
center.  A  small  magnetic  needle  will  set 
itself  tangent  to  these  circles  at  any  point. 
If  the  current  passes  up  the  wire,  as  in  Fig. 
340,  the  direction  of  the  lines  of  force  is  counterclockwise.  By  the 
direction  of  the  magnetic  lines  is  meant,  as  in  §  324,  the  direction  in 
which  the  +  end  of  the  magnetic  needle  will  point.  If  the  current 
is  sent  down  the  wire,  then  the  direction  of  the  lines  of  force  will 
be  clockwise. 

While  there  is  no  difficulty  in  showing  the  magnetic  effect  of  the 
current  in  a  single  wire  by  the  use  of  a  small  magnetic  needle  or 
compass,  it  is  necessary  to  use  a  current  of  from  20  to  30  amperes  in 
order  to  show  the  circular  character  of  the  fines  of  force  by  the  filings. 
If  a  current  of  this  amount  cannot  be  obtained,  the  same  effect  can 
be  produced  by  sending  a  current  of  one 
ampere  through  a  vertical  coil  (of  about 
25  turns)  which  pierces  the  card.  Fig. 
341  indicates  how  this  may  be  done. 

The  relation  between  the  direc- 
tion of  the  current  flowing  in  a 
conductor  and  the  direction  of  the 
resulting  lines  of  magnetic  force 
around  it,  may  be  stated  as  fol- 
lows :  Grasp  the  conductor  in  the  right  hand,  with  the  thumb 
pointing  in  the  direction  in  which  the  current  is  flowing;  then 
the  fingers  will  point  in  the  direction  of  the  lines  of  magnetic  force. 


FIG.  341 


THE   EFFECTS  OF  THE   CURRENT  365 

406.  Deflection  of  the  Needle.  —  Demonstration.  —  Couple  a 
battery  to  a  straight  wire  AB  (Fig.  342),  and  hold  it  above  and  par- 
allel to  a  magnetic  needle.  The  __^4  &  ^. 
needle  will  turn  from  its  posi- 
tion  in  the  direction  indicated 
in  the  figure.  Place  the  wire 
below  the  needle,  and  the  direc- 
tion of  its  deflection  is  reversed. 

Change  the  direction  of  the  current  in  the  wire,  and  the  needle  is 
deflected  as  at  first. 

This  demonstration  is  important;  it  shows  the  principle 
of  one  class  of  measuring  instruments.     The  relation  between 

the  direction  of  the  current 
in  the  wire  and  the  deflec- 
tion of  the  north  end  of  the 
needle  is  what  we  should 
expect  from  the  direction 
of  the  lines  of  force  around 
FlG-  343  a  current :  Place  the  right 

hand  with  the  palm  on  the  wire  and  turned  toward  the  needle, 
and  with  the  fingers  extended  in  the  direction  in  which  the 
current  is  flowing;  then  the  extended  thumb  will  point  in  the 
direction  of  the  deflection  of  the  north  end  of  the  needle. 

406.  Magnetic  Properties  of  the  Solenoid.  —  A  solenoid  is 
formed  of  a  coil  of  insulated  wire  wound  in  the  form  of  a 
cylinder  in  one  or  more 
layers. 


Demonstration.  —  Place 
upon  a  table  a  magnetic 
needle,  and  let  it  come  to  rest.  S 

Place  a  solenoid  S  with  one  end  about  two  inches  from  the  north 
pole  of  the  needle.  Close  the  key  K,  sending  the  current  through 
the  solenoid,  and  the  needle  will  be  acted  on  at  once,  being 


366 


ELECTRICITY 


FIG.  345 


either  attracted  or  repelled  according  to  the  direction  of  the  cur- 
rent in  the  coil. 

The  length  of  a  solenoid  is  usually  great  compared  with 
its  diameter,  but  its  magnetic  properties  are  still  retained 
even  if  it  is  shortened  to  a  single  turn.     Figure 
345  shows  lines  of  force  of  such  a  turn. 

An  important  use  is  made  of  the  solenoid, 
in  the  circuit  breaker  which  is  used  to  protect 
electrical  circuits  from  too  heavy  currents. 
Figure  346  gives,  in  diagram,  the  path  of  the 
current.  When  the  current  in  the  solenoid  be- 
comes too  great,  the  iron  plunger  P  is  drawn  up, 
strikes  the  brass  pin  p,  which  trips  the  catch  Ct 
that  holds  the  arm  A  in  place.  The 
spring  $,  which  is  compressed  when 
the  breaker  is  closed  by  the  handle 
H,  pushes  A  out  and  breaks  the  con- 
tact between  A  and  B.  The  amount 
of  current  required  to  pull  up  the 
plunger  P  depends  upon  its  position,  — < 
which  is  regulated  by  the  thumb- 
screw T. 

407.  The  Electromagnet.  —  If  the 

solenoid  is  provided  with  a  soft  iron 
core,  it  becomes  an  electromagnet. 
Since  the  iron  offers  a  better  path 
for  the  lines  of  magnetic  force  than 
air,  that  is,  a  path  having  less  resist- 
ance, the  introduction  of  the  iron  in- 
creases the  number  of  lines  of  force 

..  .  ...    FIG.  346.  —  Solenoid  Circuit 

^  maxwells)  that  a  certain  current  will  Breaker 


THE   EFFECTS  OF  THE  CURRENT 


367 


FIG.  347 


generate  on  passing  through  the  coil.     This    _x~- • 
means  that  the   magnetic  strength    of    the 
electromagnet  is  increased. 

Demonstrations. — Make  an  electromagnet  by 

winding  several  layers  of  insulated  copper  wire 

No.  16  around  a  wooden  spool  about  a  foot  long, 

and  putting  a  piece  of  gas  pipe  or  soft  iron  rod 

inside  the  spool  for  a  core.     Couple  with  several 

cells  of  a  battery,  and  when  the  current  is  turned 

on,  dip  the  end  of  the  core  into  a  box  of  nails; 

lift  the  magnet  and  note  the  effect  as  shown  in 

Fig.  347.    Break  the  current.    What  is  the  result  ? 
Support  the  same  magnet  vertically,  and  lay 

over  the  upper  end  a  sheet  of 
glass  (Fig.  348)  upon  the  under 
side  of  which  a  sheet  of  paper 
has  been  pasted.  Sift  over  the 
plate  an  even  layer  of  iron 
filings,  and,  tapping  the  plate 
lightly,  turn  on  the  current.  The 
lines  of  force  will  be  shown  in  a 
striking  manner. 

408.  Poles  of  an  Electro- 
magnet.— When  the  ends  of 
a  solenoid  or  an  electromagnet  are  tested  with  a  magnetic 
needle,  it  is  found  that  the  lines  of  force  pass  through  the  core 
in  the  direction  we  should  ex- 
pect from  §§  404, 405.  There- 
fore, for  determining  the  poles 
of  an  electromagnet,  the  fol- 
lowing rule  holds  :  //  the  coil 
is  grasped  in  the  right  hand 
with  the  fingers  pointing  in  the  direction  of  the  current,  then 
the  thumb  will  point  toward  the  north  pole  of  the  magnet. 


FIG.  348 


FIG.  349 


368  ELECTRICITY 

409.  The  Horseshoe  Electromagnet.  —  Since    the  object 
to  be  attained  in  an  electromagnet  is  a   strong   magnetic 
field,  the  horseshoe  form  is  the  best.     As  commonly  made, 
it  consists  of  two  spools  wound  with  insulated  wire  and 

mounted  on  two  cylindrical  cores, 
which  are  fixed  perpendicularly  into  a 
yoke  of  soft  iron  (Fig.  350) .  The  wire 
is  wound  on  the  spool  in  such  a  way 
that  if  the  cores  and  yoke  were  bent 
out  into  a  straight  line,  the  winding 
would  be  all  in  one  direction.  The  piece  of  soft  iron  often 
provided  for  the  magnet  to  attract  (at  the  ends  of  the 
cores  opposite  the  yoke)  is  called  the  armature. 

The  core  of  an  electromagnet  should  be  of  such  a  qual- 
ity of  iron  that  it  will  lose  its  magnetism,  or  become  de- 
magnetized, as  soon  as  the  current  is  stopped.  If  there  is  a 
small  amount  of  residual  magnetism  in  it  after  the  current 
is  cut  off,  so  that  it  will  not  release  the  armature  promptly, 
paper  can  be  pasted  over  the  ends  of  the  magnet  to  help 
overcome  this  defect.  Annealing  the  cores  will  sometimes 
remove  the  difficulty. 

The  number  of  lines  of 'force  passing  through  the  cores  of 
an  electromagnet  depends  upon  two  things ;  the  number 
of  turns  of  wire  and  the  current  through  each  turn.  The 
product,  called  the  ampere  turns,  is  a  measure  of  the  strength 
of  the  magnet. 

410.  The  Lifting  Magnet.  —  In   order  that   an   electro- 
magnet may  have  great  lifting  power,  the  air  gap  between 
the  iron  core  and  the  iron  to  be  lifted  should  be  as  small 
as  possible,  the  path  of  the  lines  of  force  should  be  short, 
and  the  iron  should  offer  little  resistance  to  the  lines  of  force. 


THE   EFFECTS  OF  THE   CURRENT 


369 


Figure  351  is  a  cross  section  of  an  efficient  form,  and  Fig.  352 
shows  the  magnet  in  actual  use,  in  transferring  steel  billets 
to  or  from  a  railroad  car.  The  mag- 
net is  placed  upon  the  iron  or  steel 
to  be  lifted,  the  current  is  sent  through 
the  coil,  the  magnet  and  its  load  are 
moved  by  a  crane  to  the  desired  spot, 

Current  Wires 


FIG.  351 


FIG.  352 


and  the  load  is  dropped  by  breaking  the  circuit.  If  non- 
magnetic substances  are  to  be  lifted,  they  must  be  attached 
to  an  armature. 

411.  The  Electric  Bell.—  The  com- 
mon electric  bell  is  an  application 
of  the  electromagnet.  When  the 
button  B  is  pressed,  it  closes  the  cir- 
cuit, and  the  current  enters  by  the 
+  binding  post ;  passes  around  the 
electromagnet,  then  to  the  post  P 
(Fig.  353),  through  which  runs  a  pin 
that  makes  contact  with  the  arma- 
ture of  the  magnet  by  means  of  a 
light  spring,  then  along  the  spring 
S  to  the  —  binding  post.  In  bells  having  an  iron  base 
the  base  itself  is  made  a  part  of  the  circuit.  As  soon  as 

Rev. 


FIG.  353.  —  Electric  Bell 


370 


ELECTRICITY 


the  current  passes,  the  armature  of  the  electromagnet  is 
attracted  and  the  current  is  broken  at  P.  When  this  hap- 
pens the  magnet  no  longer  attracts  the 
armature,  and  the  spring  S  carries  it 
back  against  the  post  P,  again  making 
the  circuit.  This  causes  the  bell  to  ring 
automatically  as  long  as  the  button  is 
pushed.  When  two  or  more  bells  are 
to  be  rung  from  a  single  push  button, 
'  they  should  be  coupled  in  parallel,  as 
they  will  not  ring  well  in  series  unless 
they  strike  at  exactly  the  same 
(Fig.  354). 


& 


rate 


412.  The  Electric  Telegraph.  —It  is 
evident  that  the  electric  bell  can  be 
used  for  signaling  at  a  long  distance. 
The  telegraph,  which  is  used  especially 
for  this  purpose,  depends  upon  the  same 
principle :  that  of  the  electromagnet. 
The  principal  parts  of  the  telegraph  are  the  main  battery 
and  line,  the  relay,  the  local  battery  and  circuit,  the  sounder, 
and  the  key. 


FIG.  354.  — Diagram  of 
Bells  in  Parallel 


413.  The  Key  is  simply  a  circuit  breaker  put  in  the  main 
line,  and  so  arranged  that  the  current  is  sent  every  time  the 
lever  K  (Fig.  355)  is  pressed 
down.  When  the  key  is 
not  in  use  for  sending  mes- 
sages, the  switch  S  is  closed, 
making  contact  so  that 
messages  can  be  received.  FIG.  355.— Telegraph  Key 


THE  EFFECTS  OF  THE   CURRENT  371 

414.  The  Main  Battery  consists  either  of  a  group  of  gravity 
cells  or  of  a  dynamo.     There  is  usually  a  main  battery  at 
each  end  of  the  line. 

415.  The  Line  consists  of  iron  or  copper  wire  supported 
by  glass  insulators  attached  to  the  line  poles.     At  one  termi- 
nal station  the  +  pole  of  the  main  battery  is  connected  with 
the  line  and  the  —  pole  is  connected  with  the  earth  or  is 
"  grounded,"  while  at  the  other  terminal  station  the  —  pole 
is  connected  with  the  line  and  the  +  is  grounded. 

416.  The   Relay  is  an  electromagnet  of  high  resistance 
in  series  with  the  main  line.     Its  function  is  to  make  and 
break  contact  in  the  local  circuit  which  controls  the  sounder. 
It  has  nothing  whatever  to  do  with  strengthening  the  current 
in  the  sounder,  which  gets  its  current  from  the  local  battery 
only.     When  a  current  from  the  main  line  passes  through  the 
relay,  its  armature  is  attracted,  current  from  the  local  battery 
passes  through  the  sounder  circuit,  the  sounder  armature  is 
attracted  and  makes  a  loud  click  from  which  the  message 
is  read.     The  way  in  which  this  is  done  will  be  seen  by  re- 
ferring to  Fig.  357.    The  relay  is  wound  with  a  great  many 

turns  of  fine  wire,  so  that  the 
small  main  current  may  be  able 
to  magnetize  it. 

417.  The  Sounder  is 
an  electromagnet,  in 
the  local  circuit,  from 
which  the  message  is 
read.  This  sounder  is 

FIG.  356.— Sounder 

wound  with  fewer  turns 

of  wire  of.  a  larger  size  than  that  used  in  the  relay,  because 
the  current  is  comparatively  large  in  the  local  circuit. 


372 


ELECTRICITY 


418.  Connection  and  Operation  of  the  Line.  —  Let  Fig.  357 
represent,  diagrammatically,  a  line  having  Philadelphia  and 
New  York  for  its  terminal  stations  and  Trenton  for  an  inter- 
mediate station.  The  connections  are  arranged  for  sending 
a  message  from  New  York  to  Philadelphia.  The  switch  $ 
at  Philadelphia  is  closed,  that  at  New  York  is  open.  When 


the  operator  at  New  York  presses  his  key,  the  connection  is 
made  along  the  line,  and  the  relay  at  Philadelphia  is  magnet- 
ized. The  armature  A  is  attracted,  moves  toward  the 
magnet,  and  comes  in  contact  with  the  pin  P ;  and  as  this  is 
coupled  to  one  side  of  the  local  battery  and  the  armature 
to  the  other  side  through  the  sounder,  the  local  circuit  is 
made  and  the  sounder  attracts  its  armature.  As  soon  as 
the  sender  at  New  York  releases  his  key,  the  circuit  is  broken, 
A  is  pulled  back  to  its  normal  position  by  a  spring,  the  local 
circuit  is  broken,  and  the  condition  is  just  as  it  was  before 
the  signal  was  sent. 
The  message  sent  to  Philadelphia  may  also  be  read  at 


THE  EFFECTS  OF  THE  CURRENT  373 

Trenton  ;  for  the  current  has  the  same  effect  on  any  inter- 
mediate relays  that  it  lias  on  the  Philadelphia  relay.  If 
'the  message  had  been  intended  for  Trenton,  the  New  York 
operator  would  have  first  sent  the  Trenton  "  call  "  until  the 
Trenton  operator  had  responded,  showing  that  he  would 
pay  attention. 

419.  The  Telegraphic  Alphabet.  —  Telegraphic  messages 
are  sent  by  what  is  known  as  the  Morse  alphabet.  This 
consists  of  a  series  of  dots  and  dashes  with  intervals  between 
the  letters  and  longer  intervals  between  the  words. 

In  the  first  instruments  there  was  used  a  special  receiver 
that  traced  the  dots  and  dashes  upon  a  strip  of  paper.  The 
universal  custom  now  is  to  read  by  sound. 

The  Morse  Alphabet 

U  --- 
V  - 

w- 


Z  - 


420.  Chemical  Effects.  —  Demonstrations.—  Fit  corks  to  the 
two  sides  of  a  U-tube.  Through  these  corks  pass  copper  wires  with 
platinum  terminals.  Fill  the  tube  nearly  to 
the  top  of  the  terminals  with  a  solution  of 
sodium  sulphate  (Na2S04)  colored  with  blue 
litmus.  Couple  two  or  three  cells  in  series  to 
the  copper  wires,  and  in  a  few  minutes  the 
solution  in  the  U-tube  near  the  +  terminal 
will  turn  red,  showing  the  presence  of  an 
acid,  while  the  color  at  the  —  terminal  shows 
the  presence  of  an  alkali. 

Rinse  the  U-tube  used  in  the  above  experi-  FIG.  358 


A  -  — 
B 

H  

T      . 

0-   - 
p 

C  
D- 
TC 

J     - 
J£    

T 

Q  
R- 

F  - 
G  

M- 
N  —  - 

T- 

374 


ELECTRICITY 


ment,  and  fill  it  nearly  full  of  water  to  which  a  few  drops  of  sulphuric 
acid  have  been  added.  Cut  a  notch  along  the  side  of  each  cork 
and  couple  three  dry  cells  in  series.  Bubbles  of  gas  will  be  noticed 
at  each  terminal.  Those  given  off  at  the 
+  terminal  are  oxygen  and  those  at  the  — 
terminal  are  hydrogen. 

The  relative  quantities  of  the  gases  given 
off  at  the  terminals  can  be  measured  by 
using  a  form  of  apparatus  like  that  shown 
in  Fig.  359.  This  is  known  as  Hoffman's 
apparatus,  and  with  it  the  hydrogen  col- 
lected over  the  negative  terminal  is  shown 
to  be  twice  the  volume  of  the  oxygen  col- 
lected over  the  positive  terminal. 

The  action  of  the  current  shown  in 
these  demonstrations  is  called  electrol- 
ysis, and  the  solution  in  which  this 
action  goes  on  is  an  electrolyte.     The 
FIG.  359  apparatus  used  in  electrolysis  is  called 

a  voltameter;  and  the  terminals,  elec- 
trodes. The  electrode  by  which  the  current  enters  the  elec- 
trolyte is  called  the  anode,  and  that  by  which  it  leaves,  the 
cathode.  The  parts  into  which  the  current  separates  the 
electrolyte  are  called  ions;  that  which  goes  to  the  cathode  is 
called  the  cation;  and  that  which  goes  to  the  anode  is  called 
the  onion.  From  the  direction  which  the  ions  take  in  the 
electrolyte  their  electric  condition  is  determined;  hence 
the  cation  is  considered  electropositive  and  the  anion 
electronegative. 

In  the  experiment  with  sodium  sulphate  the  Na2S04,  on 
going  into  solution,  breaks  up  into  positively  charged  ions, 
+  Na,  and  negatively  charged  ions,  —  SO4.  When  the  SO4 
ions,  sulphions,  reach  the  positive  platinum  plate,  as  they  will 
by  mutual  attraction,  they  give  up  their  negative  charge 


THE  EFFECTS  OF  THE  CURRENT  375 

and  attack  the  water,  forming  H^SCh,  and  setting  O  free. 
The  Na  ions  give  up  their  positive  charge  to  the  negative 
•  plate,  attack  the  water,  and  form  NaOH,  setting  H  free. 

421.  Electrolysis  of  Copper  Sulphate.  —  Demonstration.  — 

Send  a  current  through  a  solution  of  copper  sulphate  placed  in  the 
U-tube,  Fig.  358,  and  it  will  be  found  that  bubbles  of  oxygen  rise 
from  the  anode,  while  the  cathode  will  be  coated  with  copper. 

The  action  of  the  current  in  this  demonstration  is  to 
separate  the  CuSO4  into  +  Cu,  which  goes  with  the  current 
toward  the  cathode  and  is  deposited  upon  it,  and  —  SC>4 
which  goes  toward  the  anode  and  decomposes  the  H2O  of  the 
solution  H2SO4,  setting  oxygen  free. 

422.  Electrometallurgy.  —  If  a  copper  anode  is  used  in 
the  last  demonstration,  the  SCX  will  unite  with  it,  forming 
CuSO4,  keeping  up  the  strength  of  the  solution  and  eating 
away  the  copper.     If  a  plate  of  impure  copper  is  used  as 
the  anode,  the  copper  deposited  on  the  cathode  will  be  pure, 
the  impurities  being  left  in  the  solution. 

When  lead  ores  are  reduced  to  metallic  lead  in  a  furnace, 
there  is  usually  with  the  lead  a  small  quantity  of  silver. 
In  order  to  obtain  pure  lead  to  be  used  in  paints,  the  pig 
lead  containing  the  silver  is  used  as  the  anode,  and  a  lead 
plate  as  cathode.  When  the  current  is  sent  through  the 
bath,  pure  lead  is  transferred. from  the  anode  to  the  cathode, 
while  the  silver  is  left  in  the  bath  as  a  residue.  The  silver 
is  afterwards  recovered  from  the  solution,  and  forms  an 
important  by-product. 

423.  Electroplating  is  the  process  of  coating  one  metal 
with  another  by  means  of  the  electric  current..    The  article 
to  be  coated  is  the  cathode  of  the  cell  and  is  coupled  to  the 
anode  of  a  battery.    Copper  may  be  deposited  from  a  bath 


376  ELECTRICITY 

of  copper  sulphate,  silver  from  one  of  the  double  cyanide  of 
silver  and  potassium,  nickel  from  one  of  nickel  ammonium 

sulphate.  Nickel  plating 
is  used  to  protect  from 
oxidation  articles  made  of 
brass,  iron,  or  steel. 

In  commercial  electro- 
plating the  electrolyte  is 
"^  in  a  large  tank  along  each 

FIG.  360.  —  Tank  for  Electroplating  > 

side  of  which  runs  a  heavy 

copper  rod.  The  articles  to  be  plated  are  suspended  from 
one  rod,  and  a  plate  of  the  metal  to  be  deposited,  from 
the  other.  A  dynamo  that  gives  a  heavy  current  and  low 
voltage  is  used,  the  current  being  sent  through  the  tank 
from  the  metal  plate  to  the  articles  to  be  plated.  These 
articles  must  be  chemically  clean  on  the  surface.  The  nec- 
essary potential  difference  at  the  two  rods  varies  with  the 
metals  deposited. 

424.  Electrotyping.  —  The    process    of    electrotyping    is 
used  to  make  copies  of  type,  medals,  or  other  objects.     The 
object  to  be  copied  is  thoroughly  cleaned  and  a   mold  is 
taken  from  it  in  wax  or  plaster  of  Paris.     A  careful  dusting 
of  the  surface  with  some  conducting  substance,  as  graphite, 
is  necessary ;  then  the  mold  is  suspended  in  the  proper  solu- 
tion by  a  wire  from  the  anode  of  a  battery,  the  current  is 
turned  on,  and  the  deposit  begins.     When  the  coating  is 
thick  enough  so  that  it  can  be  taken  from  the  mold  without 
bending,  it  is  removed  and  backed  by  melted  lead  or  type 
metal. 

425.  Storage  Cells.  —  If  a  galvanometer  is  coupled  to  the 
terminals  of  a  voltameter  after  a  current  has  been  sent 


THE   EFFECTS   OF  THE   CURRENT 


377 


FIG.  361 


through  it,  the  needle  will  be  deflected,  showing  that  the 
voltameter  is  itself  capable  of  giving  out  a  current. 

Demonstrations. — Fasten  two  sheets  of  lead  to  the  opposite  sides 
of  a  wooden  support  and  suspend  them  in  a  jar  of  dilute  sulphuric 
acid.  Connect  the 
cathode  of  two  or  three 
dry  cells  coupled  in 
series,  to  one  of  the 
plates  and  the  anode 
to  one  terminal  of  a 
double  snap  switch. 
Couple  an  electric  bell 
to  the  plate  and  switch 
as  shown  in  Fig.  361. 
Send  the  current  from 
the  battery  through 
the  cell  for  a  short 

time  —  a  second  or  two  will  answer  —  then  snap  the  switch,  the 
battery  will  be  cut  out,  the  bell  will  be  thrown  in  circuit  with  the 
cell  and  will  begin  to  ring.  The  action  will  be  strong  at  first  and 
gradually  die  out. 

Repeat  and  note  the  effect  of  the  length  of  time  the  battery  is 
sending  a  current  upon  the  length  of  time  the  bell  will  ring. 

Repeat,  using  a  2- volt,  1-candle  power  incandescent  lamp  instead 
of  the  bell. 

It  will  be  observed  that  there  is  a  vigorous  production  of 
oxygen  from  the  anode  and  of  hydrogen  from  the  cathode  of 
the  lead-sulphuric  acid  cell.  The  oxygen  combines  with  the 
lead  of  the  anode  forming  lead  peroxide  (PbO2)  which  covers 
the  plate  a  chocolate  brown.  When  the  bell  is  put  in  the 
circuit,  the  current  passes  through  the  cell  in  the  opposite 
direction  and  the  lead  peroxide  on  the  anode  is  changed  to  a 
spongy  form  of  lead.  Plante  was  the  first  to  discover  this 
effect  and  devised  this  form  of  battery  for  the  storing  of 


378 


ELECTRICITY 


electrical  energy.  In  recent  forms  of  this  battery  the  lead 
plates,  or  grids,  are  grooved  in  such  a  way  that  the  grooves 
can  be  filled  with  a  paste  of  red  oxide  of  lead  for  the  posi- 
tive electrode  and  litharge  for  the  negative. 


FIG.  362 


FIG.  363 


FIG.  364 


There  are  many  types  of  storage  cells  in  practical  use. 
Figure  362  shows  the  positive  and  Fig.  363  the  negative  elec- 
trode of  the  chloride  accumulator  cell, 
and  Fig.  364  shows  one  of  the  smaller 
cells  ready  for  use.  The  large  size  of 
the  plates  reduces  the  in- 
ternal resistance  of  the 
cell  and  makes  a  heavy 
current  possible. 

Storage  batteries  are 
used  as  the  motive  power 
in  electric  automobiles 
and  trucks.  An  efficient 
type  is  the  Edison  cell 
(Fig.  365),  in  which  the 
liquid  used  is  a  solution 
of  caustic  potash  and  the 
electrodes  are  nickel  hy- 
drate and  iron  oxide,  the  FlG-  366.— 

FIG.  365.— Edison  Stor        .  .    .    ,     .          .  ..  Steel      Con- 

age  Cell  nickel   being  the  positive      tainingCan 


THE  EFFECTS  OF  THE   CURRENT  379 

electrode  and  the  iron  the  negative.  The  containing  cans 
(Fig.  366)  are  made  of  corrugated  sheet  steel  which  secures 
the  cells  against  breakage. 

Questions 

1.  Which  will  affect  the  heating  of  a  wire  more,  to  double  its 
resistance  or  to  double  the  current  passing  through  it  ? 

'  2.  Why  does  a  fuse  wire  melt  on  an  electric  circuit  when  the 
copper  wire  carrying  the  current  does  not  ? 

3.  Describe  a  way  of  determining  the  direction  of  the  current  in 
a  wire  that  is  concealed  under  a  molding. 

4.  Suppose  Fig.  367  to  represent  the  end  of  a  horseshoe  magnet 
with  the  current  passing  in  the  coils  in  the  direction  indicated  by  the 
arrows.     Apply  the  rule  for  finding  the  polarity 

of  an  electromagnet  and  mark  the  poles.     Write 

a  new  rule  which  will  show  the  relation  between 

the  polarity  and  the  clockwise  or  counter-clock-          ~FIG  367 

wise  passing  of  the  current  around  the  core. 

5.  Suppose  a  current  is  passing  in  a  clockwise  direction  around  a 
coil  of  two  or  three  turns  of  wire  hanging  in  a  vertical  plane.     What 
will  be  the  direction  of  the  magnetic  axis  of  the  coil  ? 

6.  Name  four  uses  of  the  lifting  electromagnet. 

7.  What  kind  of  iron  should  be  used  for  the  core  of  an  electro- 
magnet?   Why? 

8.  What  is  the  source  of  current  for  the  relay  of  a  telegraph 
line? 

9.  What  is  the  source  of  current  for  the  sounder? 

10.  How  could  a  silver  cup  be  given  a  gold  lining  by  the  electric 
current  ? 

11.  What  is  stored  in  the  storage  cell,  electricity  or  electric 
energy?' 

Problems 

1.  How  many  calories  will  be  developed  in  a  resistance  of  15 
ohms  by  a  current  of  9  amperes  flowing  for  20  min.  ? 

2.  A  110-volt  lamp  requires  a  current  of  0.5  ampere  and  its  hot 
resistance  is  220  ohms.    Five  of  these  lamps  are  used  in  a  room  for 
2.5  hr.    How  much  heat  is  developed? 


380  ELECTRICITY 

3.  How  many  calories  of  heat  will  be  generated  by  an  electric 
toaster  the  resistance  of  which  is  20  ohms  when  carrying  a  current 
of  5.5  amperes  for  5  minutes?    What  voltage  will  be  required? 

4.  100  ft.  of  copper  wire  No.  30  is  joined  in  series  with  100  ft.  of 
iron  wire  No.  30.    How  many  calories  are  developed  in  each  wire 
per  hour  when  a  current  of  2  amperes  is  sent  through  it? 

6.  To  what  temperature  will  1  liter  of  water  at  8°  C.  be  heated 
in  5  minutes  in  an  electric  water  heater  which  takes  11  amperes  on 
a  110-volt  circuit?  (Make  no  correction  for  loss  in  the  heater.) 


IV.    ELECTRICAL  MEASUREMENTS 

426.  Electrical  Quantities.  —  The  three  quantities  most 
necessary  to  measure  in  electricity  are  current,  resistance, 
and  electromotive  force. 

427.  Instruments  Used  in  Measurements ;  Galvanometers. 
—  A  galvanometer  is  an  instrument  that  shows  the  intensity 
of  a  current  passing  through  it,  by  the  amount  of  the  deflec- 
tion of  a  needle  (§  405)  or  other  moving  part.     It  is  cali- 
brated by  determining  experimentally  the  relation  between 
the  current  and  the  corresponding  deflection,  and  indicating 
this  on  a  graduated  scale.     A  galvanometer  of  small  resist- 
ance, if  calibrated  to  read  in  amperes,  is  called  an  ammeter. 

If  the  resistance  of  a  galvanometer  is 
known,  the  potential  difference  that 
sends  the  current  can  be  readily  de- 
termined. A  galvanometer  of  high  re- 
sistance, calibrated  to  read  directly  in 
volts,  is  called  a  voltmeter. 

The  detector  galvanometer  (Fig.  368),  or 

galvanoscope,  is  used  rather  to  show  the  presence  of  a  current  than 
to  measure  its  intensity.     A  simple  form  can  be  made  by  using  a 


ELECTRICAL  MEASUREMENTS 


381 


FIG.  369 


small  compass  for  the  needle,  setting  this  in  a  block,  and  winding 
a  few  turns  of  insulated  wire  around  it.  By  connecting  the  ends 
of  the  coil  to  binding  posts,  the  instrument  is  completed  and  will 
answer  for  many  experiments. 

428.  The  Solenoid  Galvanometer.  —  One  principle  used 
in  the  construction  of  galvanometers  is  that  which  determines 
the  following  phenomenon :  If  an 
iron  rod  is  suspended  with  one  end 
inside  a  coil  of  wire,  the  rod  will  be 
pulled  into  the  coil  as  soon  as  a  cur- 
rent is  sent  through  the  wire  —  the 
strength  of  the  pull  depending  on 
the  strength  of  the  current  used. 

One  advantage  that  the  instrument 
has  is  that  its  controlling  force  is  the 
action  of  gravity  upon  the  weight 
on  the  balance  arm.  This  insures  that  after  its  calibration 
has  once  been  made  it  will  remain  constant.  Figure  369 
represents  a  commercial  ammeter  made  on  this  principle. 
It  will  be  observed  that  the  divisions  on  the 
scale  are  not  equal.  This  is  due  to  the  fact 
that  when  the  core  is  drawn  into  the  coil,  it  is 
moving  into  a  stronger  magnetic  field. 

423.  The  d'Arsonval  Galvanometer. — An- 
other principle  used  in  the  construction  of 
galvanometers — a  most  important  one — is  em- 
ployed in  the  instrument  shown  in  Fig.  370. 
Between  the  poles  of  a  horseshoe  magnet  placed 
vertically  there  is  fixed  an  iron  cylinder  7.  A 
coil  of  fine  wire  wound  on  a  thin  copper  frame  is  suspended 
from  the  point  A,  so  that  it  will  swing  freely  between  the 
cylinder  and  the  magnet  poles.  When  a  current  is  sent 


FIG.  370 


382 


ELECTRICITY 


through  it,  the  coil  becomes  a  magnet  with  its  poles  in  a 
line  perpendicular  to  the  line  joining  the  poles  of  the  horse- 
shoe magnet,  and  at  once,  because  of  the  influence  of  the 
horseshoe  magnet,  it  is  deflected.  The  controlling  force  is 
the  torsion  of  the  wire  supporting  the  coil.  The  readings 
are  taken  either  from  a  pointer  and  a  scale,  or  from  the 
reflection  of  a  fixed  scale  from  a  mirror  fastened  to  the  coil 
at  the  point  C.  This  instrument  has  the  advantage  of  being 

dead  beat ;  that  is,  it  will  come 
to  rest  quickly  without  vibra- 
tions. 

Figure  371  shows  how  the 
d'Arsonval  principle  is  applied 
in  a  commercial  voltmeter.  The 
wire  suspension  is  replaced  by  a 
spiral  spring  which  serves  to 
carry  the  current  and  control 
the  position  of  the  pointer.  The 
coil  is  at  right  angles  to  the 
pointer  and  its  axis  is  held  be- 
tween jeweled  pivots.  The  mag- 
netic field  is  strengthened  by  soft  iron  pole  pieces  bolted 
to  the  magnet  and  nearly  surrounding  the  coil. 

430.  The    Measurement   of    Potential   Difference.  —  A 

voltmeter  is  a  high  resistance  galvanometer  and  hence  takes 
so  little  current  that  it  does  not  materially  change  the  differ- 
ence of  potential  of  the  points  it  connects.  It  is  for  this 
reason  that  a  voltmeter  will  indicate  nearly  the  E.  M.  F. 
of  a  cell  (§  394).  In  measuring  the  difference  of  potential 
between  the  points  in  a  circuit,  the  voltmeter  is  connected 
with  them  in  parallel. 


FIG.  371 


ELECTRICAL  MEASUREMENTS 


383 


431.  The  Measurement  of  Current.  —  A  current  of  elec- 
tricity is  generally  measured  by  an  ammeter,  or  low  resistance 
galvanometer,  put  in  series  in 

the  circuit.  Its  resistance  is 
so  low  that  its  introduction 
into  a  circuit  usually  makes 
no  .material  change  in  the  cur- 
rent  of  that  circuit. 

FIG.  372 

Another  method  of  meas- 

uring current  is  to  measure  the  potential  difference  at  the 
ends  of  a  known  resistance  when  the  current  is  passing 
through  it  (Fig.  372).  Many  commercial  ammeters  are 
made  on  this  plan.  The  resistance  must  be  accurately 
known  and  a  delicate  millivoltmeter  used.  If  R  equals 
0.001  ohm  and  each  scale  division  of  the  millivoltmeter  in- 
dicates a  fall  of  potential  of  0.001  volt,  then  the  current  in 
the  line  is  1  ampere  per  scale  division.  If  R  equals  0.01  ohm 
and  the  millivoltmeter  is  calibrated  as  before,  the  current 
is  0.1  ampere  per  scale  division. 

432.  The  Resistance  Box.  —  Resistances  may  be  measured 
by  comparing  them  with  known  resistances.     These  known 

resistances  are  usually 
made  of  coils  of  resistance 
wire  contained  in  a  box 
like  that  shown  in  Fig. 
373.  For  all  coils  except 
those  that  are  of  very 
small  resistance,  a  wire  is 

a     high 


FIG.  373.  -Resistance  Box 

specific  resistance,  i.e.,  one  in  which  the  value  of  K  (§  391) 
is  high,  —  such  as  German  silver.     For  all  coils,  however,  it 


384 


ELECTRICITY 


FIG.  374 


is  best  to  use  a  wire  that  has  a  low  temperature  coefficient 
(§  391).  An  alloy  called  platinoid,  which  has  a  temperature 
coefficient  less  than  half  that  of  German  silver,  is  frequently 
used.  When  the  terminals  of  a  battery 
are  connected  with  the  binding  posts 
of  the  box,  the  amount  of  resistance 
introduced  into  the  circuit  is  deter- 
mined by  the  number  of  plugs  that 
are  taken  out.  If  all  the  plugs  are  in 
the  box,  the  resistance  is  practically 
zero.  If  the  plug  T  (Fig.  374)  corre- 
sponding to  the  1-ohm  coil  is  pulled  out, 
the  current,  in  going  from  the  piece  A  to  the  piece  B,  must 
go  through  that  coil,  so  that  the  resistance  is  1  ohm.  The 
resistances  are  generally  0.1,  0.1,  0.2,  0.3,  and  0.4  ohm ;  1,  2, 
3,  and  4  ohms ;  10,  20,  30,  and  40  ohms ;  and  100,  200,  300, 
and  400  ohms.  This  makes  it  possible  to  introduce  any 
number  of  ohms  from  0.1  ohm  to  1111.1  ohms.  The  coils 
are  wound  double,  as 
shown  in  Fig.  374,  to  keep 
the  coil  from  being  a  mag- 
net as  soon  as  a  current 
passes  through  it  (§  406), 
and  also  to  prevent  self-in- 
duction, a  phenomenon 
that  will  be  discussed 
later. 

If  the  resistance  coils  are 
to    be    used    as    standards,  FIG.  375 

great  care  is  taken  to  prevent 

accidental  changes  in  their  resistance.     Such  a  coil  shown  in  Fig. 
375  is  wound  on  a  cylinder  which  is  inclosed  in  a  metal  tube.    This 


ELECTRICAL  MEASUREMENTS 


385 


tube  is  pierced  with  holes  and  is  immersed  in  oil  to  keep  the  tem- 
perature of  the  coil  constant.  A  thermometer  can  be  inserted 
through  the  hole  in  the  top  on  removing  the  plug.  The  terminals 
T  of  the  coil  are  very  heavy,  are  carefully  insulated,  and  contact 
is  made  by  the  use  of  mercury  cups. 

The  rheostat  is  a  kind  of  resistance  box  used  for  regulating 
dynamo  and  motor  currents.  The  common  ironclad  rheostat  con- 
sists, of  resistance  wire  wound  in  such  a  way  that  it  can  be  put  into 
or  taken  out  of  a  circuit 
by  moving  a  metallic  arm 
over  a  set  of  contact  points. 

Fig.  376  shows  the  face 
surface  of  a  cast-iron  en- 
ameled rheostat,  Fig.  377 
shows  the  under  side.  The  pjG  375  YIG.  377 

resistance  wire   is    entirely 

embedded  in  the  enamel,  while  the  contact  points  project  through 
it.  The  position  of  the  arm  determines  the  amount  of  resistance  in 
the  circuit. 

433.  The  Fall  of  Potential  along  a  Conductor. — Demonstra- 
tion. —  Stretch  a  high-resistance  wire  1  m.  long  on  a  board  between 
two  binding  posts  A  and  B  (Fig.  378).  Climax  wire  No.  18,  or 


':,..,.  ...;';.,.  j    vl 

—  Y 

jl 

I 

/ 

(/           9            8             7             6 

5            4             3             2             1             1 

|B      '       '       '       ' 

'         A 

FIG.  378 


German  silver  No.  24,  will  answer.     Couple  a  half  dozen  or  more 
cells  to  the  binding  posts  with  a  snap  switch  in  the  circuit.    Couple 


Rev. 


386 


ELECTRICITY 


one  terminal  of  a  low-reading  voltmeter  to  A  and  the  other  terminal 
to  a  wire  that  can  be  touched  to  the  wire  AB  at  any  point.  On 
sending  the  current  through  A  B  and  touching  the  voltmeter  wire  to 
B  the  voltmeter  reading  will  show  the  fall  of  potential  for  the  whole 
length  of  AB.  Touch  the  wire  at  the  points  9,  8,  7,  and  the  reading 
of  the  voltmeter  will  be  nine  tenths,  eight  tenths,  and  seven  tenths, 
respectively,  of  the  reading  for  AB.  In  order  to  prevent  the  polar- 
ization of  the  cells  the  current  should  be  left  on  only  just  long  enough 
to  get  each  reading. 

It  will  be  found  that  the  fall  of  potential  is  directly  pro- 
portional to  the  length  of  the  wire. 

434.  The  Measurement  of  Resistance.  —  (a)  The  Fall  of 
Potential  Method  is  well  adapted  to  the  requirements  of 
practical  electricians,  because  the  only  instruments  needed 
are  an  ammeter  and  a  voltmeter. 

Demonstration.  —  Couple  an  ammeter  A  (Fig.  379)  in  series  with 
the  resistance  R  to  be  measured.  To  the  terminals  B  and  C  of  this 

resistance  couple  a 
voltmeter  V,  as 
shown.  Make  the 
current  by  the 
switch  S,  and  read 
both  instruments  at 
the  same  time.  Sub- 
stitute these  read- 
ings in 

E       V 


FIG.  379 


derived  from  Ohm's 
Law,  and  the  value 
of  R  is  determined. 

It  is  to  be  observed  that  the  reading  of  the  ammeter  gives 
the  sum  of  the  currents  through  the  resistance  R  and  through 


ELECTRICAL  MEASUREMENTS 


387 


the  voltmeter.  On  account  of  the  high  resistance  of  the  volt- 
meter, the  current  will  usually  be  so  small  that  it  may  be 
'neglected. 

(6)  The  Method  of  the  Wheatstone  Bridge.  —  The  voltmeter 
circuit  from  the  point  B  to  the  point  C  in  Fig.  379  is  called 
a  shunt  circuit,  or  a  parallel  circuit. 

Wheatstone  made  use  of  the  fall  of  potential  in  parallel 
circuits  for  the  measurement  of  resistance.  When  two  points 
A  and  B  (Fig.  380)  are  con- 
nected by  two  parallel  circuits, 
the  total  fall  of  potential  in 
the  upper  branch  AxB  is  equal 
to  the  total  fall  in  the  lower 
branch  AyB.  There  must  be  a 
point  y  in  the  lower  branch 
where  the  fall  of  potential  from 
A  is  exactly  the  same  as  the  fall  of  potential  in  the  upper 
branch  from  A  to  x ;  so  that  the  points  x  and  y  will  have 
the  same  potential.  If,  then,  the  points  x  and  y  are  con- 
nected by  a  wire,  no  current  will  flow  in  the  wire.  If,  how- 
ever, a  wire  is  connected  from  x  to  a  point  z  between  A  and 

Illh 


FIG.  380 


r' 


FIG.  381 


y,  a  current  will  flow  from  2  to  x.  If  the  connection  is 
made  to  a  point  w,  between  y  and  B,  the  flow  will  be  from  x 
to  w.  By  the  introduction  of  a  galvanometer  in  the  con- 
ductor xy,  the  proper  position  of  y  in  which  no  current 


38S 


ELECTRICITY 


passes  in  xy  can  readily  be  determined,  and  when  this  is 
found,  the  resistance  of  Ax  :  the  resistance  of  xB  =  the 
resistance  of  Ay  :  the  resistance  of  yB. 

In  the  slide  wire  Wheatstone  bridge  (Fig.  381)  the  circuit 
AYB  is  a  single  wire  of  uniform  diameter;  hence  its  re- 
sistance is  proportional  to  its  length,  and  the  proportion 
becomes  r:r'=  1:1',  in  which  r  and  rf  are  resistances  and 
I  and  /'  lengths.  The  key  k  is  used  to  make  contact  with 
the  wire  in  determining  the  position  of  Y.  For  XB  is 
put  the  resistance  box,  while  AX  is  the  resistance  to  be 
measured. 


B 


FIG.  382.  —  A,  Wheatstone  Bridge  ;  B,  Battery  ;  C,  Galvanometer  ;  D,  Re- 
sistance Box  ;  E,  Battery  Key  ;  F,  Galvanometer  Key ;  G,  Material  to  be 
tested  ;  HH,  Spools  of  proportional  resistance 

Figure  382  shows  a  form  of  Wheatstone  bridge  in  which 
the  slide  wire  is  replaced  by  spools  of  resistance  wire  HH. 
These  can  be  put  into  the  circuit  by  taking  out  the  short- 
circuiting  plugs  and  any,  or  all  of  them,  can  be  used. 

435.  The  Combined  Resistance  of  Circuits  in  Series.  — 
The  resistance  of  100  feet  of  a  given  wire  is  twice  the  resist- 
ance of  fifty  feet  of  the  same  wire.  This  is  evident  when  we 

consider  the  expression  for  the  resistance  of  a  wire  R  =  K  —  • 

Since  the  resistance  is  directly  proportional  to  the  length, 
the  final  resistance  is  the  same  whether  the  wire  is  all  in  one 


ELECTRICAL  MEASUREMENTS 


389 


FlG-  383 


piece  or  in  two  pieces  joined  together  end  to  end.  When 
conductors  are  coupled  in  series  (Fig.  383),  each  adds  its  own 
•resistance,  so_  that  the 
combined  resistance  or 
circuits  in  series  is 

D  I        /      I         //  ' 

R  =  r  +  r'  +  r"  etc.,  in 

which  r,  r',   and  r"  are  the  individual  resistances  of  the 

circuits  that  are  joined  in  series. 

436.  The  Combined  Resistance  of  Parallel  Circuits  is 
always  less  than  that  of  either  circuit  alone.  The  reason  for 
this  is  evident  when  we  consider  the  expression  for  the  re- 


sistance of   a  wire,  R  =  K-- 


The  putting  of  two  wires  in 


parallel,  in  place  of  one  of  them,  is  equivalent  to  increasing 
the  diameter  of  that  one. 

Demonstration.  —  Wind  a  coil  of  iron  wire  No.  18  and  couple  its 
ends  to  two  binding  posts  A  and  B,  Fig.  384.  Measure  its  resistance. 
Wind  a  second  coil  of  No.  18  copper  wire,  couple  it  to  A  and  B  and 


FIG.  384 

measure  its  resistance.  Couple  both  coils  to  A  and  B  and  measure 
the  combined  resistance.  The  last  resistance  will  be  less  than  either 
of  the  others. 

A  careful  study  of  the  results  of  the  above  demonstration 
will  help  the  student  to  understand  the  conditions  which 
govern  the  resistance  of  parallel  circuits. 

To  find  an  expression  for  the  combined  resistance  of  a  cir- 


390  ELECTRICITY 

cuit  and  its  shunt,  we  can  take  the  case  of  a  galvanometer 
with  its  shunt  (Fig.  385).    The  current  passing  through  the 

galvanometer    may    be   written 

V 
G  =  —  ,  in  which  G  is  the  cur- 

g 

rent,  g  the  resistance  of  the  gal- 
vanometer and  V  the  potential 
difference  at  its  terminals.  The 
current  through  the  shunt  may 

V  V 

be  written  S  =  —  .     The  entire  current  will  be  I  =  -~  ,  in 

which  R  is  the  combined  resistance  of  the  galvanometer 
and  its  shunt. 
Since  I 


«  =  -  +  —  ,and  •=  =  -  +  -;  whence,  R  =  —  r~-         (59) 
R       g        s  R      g       s  g  +  s 

In  general,  the  parallel  resistance  of  two  circuits  is  the 
product  of  the  two  resistances  divided  by  their  sum.  The 
parallel  resistance  of  several  circuits  is  found  by  finding  the 

value  of  R  in  the  expression  -^  =  -  +  -+—,  +  -777,  etc.     In 

R     r     r      r       r 

the  case  of  any  number  of  equal  resistances,  incandescent 

lamps  for  example,  the  parallel  resistance  of  n  lamps  is  —  th 
the  resistance  of  a  single  lamp. 

The  arrangement  shown  in  Fig.  385  is  frequently  used 
when  we  wish  to  measure  a  current  greater  than  the  gal- 
vanometer will  carry  safely.  A  shunt  that  will  carry  -f$  of 
the  current,  so  that  the  galvanometer  will  read  yV  ° 
true  value  of  the  current,  is  called  a  tenth  shunt. 


437.  The  Resistance  of  a  Cell  may  be  found  by  measuring 
its  E.  M.  F.  with  a  high-resistance  voltmeter  (§  430),  and 


ELECTRICAL  MEASUREMENTS  391 

then  measuring  the  current  it  will  send  through  an  am- 

meter, the  resistance  of  which  is  known.     Ohm's  Law  may 
I  ••"'  '  77* 

be  written  in  the  form  I  =  -=r—  —  ,  in  which  R  is  the  exter- 

H  H-  r 

nal  resistance  and  r  the  internal  resistance  •  from  this, 


For  example,  if  the  voltmeter  reads  1.1  volts,  the  ammeter  0.4 
ampere,  and  the  resistance  of  the  ammeter  is  0.  1  ohm,  we  have 

r  =  ti  -  0.1  =  2.65  ohms. 

In  practice  the  resistance  of  the  ammeter  is  often  as- 
sumed to  be  zero,  and  the  internal  resistance  is  taken  as. 
E 

-r 

438.  The  Energy  of  Electric  Currents.  —  The  energy  re- 
quired to  send  a  current  varies  directly  as  the  current  and 
also  as  the  potential  difference.  When  a  difference  of  po- 
tential at  the  terminals  of  a  circuit  is  1  volt  and  this  sends  a 
current  of  1  ampere  through  the  circuit,  the  power  developed 
is  1  watt,  or  j%$  horse  power  (§  78).  In  any  circuit  the 
number  of  watts  equals  the  number  of1  volts  X  the  number 
of  amperes;  i.e.,  W  =  VA.  The  number  of  watts  required 
to  burn  a  certain  tungsten  lamp  in  which  a  current  of  0.363 
ampere  is  used,  on  a  110-  volt  circuit,  will  be  110  X  0.363 
=  40  watts.  The  practical  unit  of  power  is  the  kilowatt,  equal 
to  1000  watts.  The  kilowatt  equals  f  horse  power  and  one 
horse  power  equals  f  kilowatt.  The  practical  unit  of  work 
is  the  kilowatt  hour,  or  the  work  done  in  one  hour  at  the  rate 
of  1  kilowatt  —  namely  3,600,000  joules. 

The  work  done  in  burning  incandescent  lamps  is  measured 


392  ELECTRICITY 

in  watt  hours ;  the  charging  of  a  storage  battery,  in  kilowatt 
hours.  A  battery  of  55  cells,  charged  from  a  circuit  giving 
a  potential  drop  of  110  volts  across  the  battery  terminals  and 
sending  a  current  of  25  amperes  through  the  cells  for  one 
hour,  would  have  2.75  kilowatt  hours  of  work  done  on  it. 

Questions 

1.  Suppose    you  should  couple    a    detector    galvanometer    to 
a  circuit  of  unknown  polarity.     How  would  you  determine  the 
polarity  ? 

2.  Why  is  the  iron  core  of  a  solenoid  galvanometer  drawn  into 
the  coil? 

3.  Does  the  direction  in  which  the  current  passes  through  the 
movable  coil  of  a  d'Arsonval  galvanometer  make  any  difference  with 
the  direction  in  which  it  turns? 

4.  What  would  be  the  effect  of  leaving   out  the  shunt  of  the 
millivoltmeter  when  using  it  to  measure  current  ? 

6.  Why  must  the  ammeter  and  voltmeter,  used  in  the  fall  of 
potential  method  of  measuring  resistance,  be  read  at  the  same  time  ? 

6.  Why  do  two  wires  coupled  in  series  have  a  greater  resistance 
than  either  wire  ? 

7.  Why  do  two  wires  coupled  in  parallel  have  a  smaller  resistance 
than  either? 

8.  What  method  should  you  use  in  measuring  the  resistance  of 
a  galvanometer?    Why? 

Problems 

1.  A  wire  2  m.  long  has  a  potential  difference  at  its  ends  of  6.3 
volts.    What  is  the  potential  difference  between  one  end  of  the  wire 
and  points  0.6  m.,  0.9  m.,  1.5  m.,  and  1.8  m.  distant?    Make  a 
curve  to  show  the  results. 

2.  A  certain  lamp  requires  6.6  amperes  and  80.5  volts  to  run  it 
properly.    What  is  the  resistance  of  the  lamp? 

3.  Suppose  the  lamp  in  problem  2  is  coupled  to  a  110-volt  circuit. 
What  resistance  must  be  put  in  series  with  it? 

4.  The  difference  of  potential  at  the  ends  of  a  branched  circuit 
of  9  and  13  ohms  is  11  volts.    What  is  the  current  through  the  9-ohm 


INDUCED    CURRENTS    AND    THE    DYNAMO        393 

branch?    Through  the  13-ohm  branch?     What  is  the  total  current? 
What  is  the  combined  resistance  of  the  two  branches? 
•      6.  A  resistance  board  (Fig.  386)  has  in  it  five  110-volt,   16- 
candle-power  lamps  and  one  55-volt  lamp.     The  110-volt  lamps 
require  a  current  of  0.5  am- 
pere each.    What  is  the  re- 
sistance    per     lamp?      The 
55-volt  lamp  requires  a  cur- 
rent of  1  ampere.    What  is  FlG  386 
its  resistance?    What  is  the 

resistance,  in  parallel,  of  2  of  the  110-volt  lamps?     Of  3?     Of  4? 
Of  5?    Of  one  110-volt  lamp  and  the  55-volt  lamp  in  parallel? 

6.  An  electric  toaster  requires  6  amperes  on  a  110-volt  circuit. 
How  many  watts  of  electric  power  will  it  use?     What  will  it  cost 
to  run.it  10  minutes  each  morning  for  30  mornings  if  electric  energy 
costs  9  cents  per  kilowatt-hour? 

7.  What  is  the  resistance  of  a  tenth  shunt  for  a  galvanometer, 
the  resistance  of  which  is  13  ohms? 

8.  A  storage  battery  is  to  be  charged  from  a  110-volt  circuit. 
The  charging  current  must  not  exceed  5  amperes.     If  the  internal 
resistance  of  the  battery  is  2.5  ohms,  what  external  resistance  must 
be  placed  in  series  with  the  battery?    How  many  110-volt  16- 
candle-power  lamps  in  parallel  would  give  the  required  resistance? 

9.  The  slide  wire  in  a  Wheatstone  bridge  is  1  m.  long.     A  balance 
is  obtained  when  452  mm.  of  the  slide  wire  corresponds  to  2  ohms  in 
the  resistance  box  and  the  rest  of  the  wire  corresponds  to  a  coil  of 
unknown  resistance.     Find  the  resistance  of  the  coil. 

V.    INDUCED  CURRENTS  AND  THE  DYNAMO 

439.  Parallel  Currents.  —  Demonstration.  —  Wind  a  spiral  3 
cm.  in  diameter,  of  about  thirty  turns  of  No.  24  insulated  copper 
wire.  Suspend  it  from  a  rod  and  couple  the  upper  end  to  the  +  pole 
of  a  battery.  Straighten  out  a  short  piece  of  the  lower  end  of  the 
coil  and  let  it  dip  into  a  drop  of  mercury  which  is  connected  with  the 
-  pole  of  the  battery.  When  the  current  is  turned  on,  the  spiral 
will  shorten  and  lift  the  end  from  the  mercury.  A  spark  will  pass, 
then  the  spiral  will  lengthen,  the  point  will  again  touch  the  mercury, 
and  the  action  will  be  repeated. 


394 


ELECTRICITY 


'©)(©) 

>    ^-' 


FIG.  388 


This  demonstration  shows,  in  a  simple  way, 
one  result  of  the  mutual  action  of  parallel 
currents.  Experiment  ^4  3 

has  proved  the  truth  of 
the  following  law : 

I.    Parallel  currents 
flowing  in  the  same  direc- 
tion attract  each  other,  and  ,*-- — ^-v 
those  flowing  in  opposite  {  (  Q  Q  v 
directions  repel  each  other.          \^- — •• -'' 

It    will   be    observed  FlG' 389 

that  this  law  is  directly       ^^ 
opposite  in  form  to  the 
statement  of  the  funda- 
mental   law    that    lines 
of  magnetic  force  going 

in  the  same  direction  repel  each  other  (§327).     That  the 

two  laws  are  statements  of  the  same  phenomena,  however, 

can  be  shown  by  a  consideration  of  Figs.  388,  389,  390. 

In  the  case  of  A  and 

jB,  which  are  carrying 

currents  in  the  same 

direction  (toward  the 

observer),   the   lines 

of  force  between  the 

wires    are    going   in 

opposite    directions. 

This  means  that  the 

lines    of    force    will 

run  into  each  other 

and,  by   shortening,  FIG.  391 


FIG.  387 


FIG.  390 


INDUCED  CURRENTS  AND  THE  DYNAMO      395 


tend  to  bring  the  wires  together,  with  the  lines  of  force  in- 
closing both,  as  in  Fig.  389. 

In  conductors  C  and  D,  in  which  the  currents  are  moving 
in  opposite  directions,  the  lines  of  force  between  the  wires 
are  in  the  same  direction,  and  repulsion  is  the  result.  Among 
the  many  ways  of 
showing  this  tendency 
of  the  lines  of  force  to 
contract  and  move  the 
conductor  is  the  fol- 
lowing : 

Demonstration. — 

Suspend  a  coil  of  loosely 

wound  insulated  copper 

wire   over  a  horizontal 

glass  tube  as  shown  in  FIG.  392 

Fig.  391.     On  sending  a  current  through  the  coil  the  wires  will 

move  together,  Fig.  392.     An  iron  rod  placed  in  the  tube  will 

bring  the  wires  together  more  quickly. 

440.  Induced  Currents.  —  (a)  When  the  Conductor  is 
Moved.  —  Demonstration.  —  Make  a  coil  of  insulated  copper  wire  No. 
30,  that  will  slide  easily  over  a  long  bar  magnet,  and  couple  it  to  a  sen- 
sitive galvanometer.  Place  the  coil  around  the  magnet  at  the  middle 

and  when  the  needle  of 
\  \  \  the  galvanometer  is  quiet, 
suddenly  slip  the  coil  off 
the  +  end  of  the  magnet. 
The  galvanometer  will 
give  a  sudden  throw,  and 
then  gradually  come  to 
rest  at  zero.  Place  the 
coil  again  at  the  middle  of 
the  magnet,  and  slip  it  off  over  the  -  end.  Again  there  will  be  a 
throw  of  the  needle,  but  in  the  opposite  direction.  Taking  the 


FIG.  393 


396 


ELECTRICITY 


magnet  in  one  hand  and  the  coil  in  the  other,  slip  the  coil  on  the 
magnet  from  the  —  end.  Note  the  direction  of  the  deflection. 
Again,  slip  the  coil  on  the  magnet  from  the  +  end,  and  notice  the 
direction  of  the  deflection. 

The  currents  produced  in  this  demonstration  are  induced 
currents,  and  they  are  produced  by  the  cutting  of  magnetic 
lines  of  force  by  an  electrical  conductor.  The  demonstration 
shows  that  the  currents  produced  depend  for  their  direc- 
tion upon  the  direction  in  which  the  conductor  cuts  the 

lines  of  force.  By  varying 
the  speed  of  slipping  off  the 
coil,  we  shall  find  that  the 
amount  of  current  depends 
upon  the  number  of  lines  cut 
in  a  given  time.  The  rela- 
tion between  the  direction  of 
motion  of  the  conductor,  the 
direction  of  the  lines  of  force, 
and  the  direction  of  the  in- 
duced current,  is  shown  in 
Fig.  394.  If  a  conductor  AB  is  held  horizontally  and  al- 
lowed to  fall  in  a  magnetic  field,  cutting  the  lines  of  force 
as  shown,  then  there  will  be  set  up  at  the  ends  A  and  B  a 
difference  of  potential  which  will  tend  to  send  the  current 
from  A  to  B.  This  important  law  may  be  stated  as  follows  : 

//  a  person,  holding  a  conductor  horizontally,  stands  at  a 
+  pole  looking  in  the  direction  of  the  lines  of  force,  and  lets 
the  conductor  fall,  the  induced  current  will  flow  toward  the 
right  hand. 

Various  other  rules  have  been  devised  to  express  the  law. 
One  of  these  i§  as  follows :  Hold  the  thumb  and  the  first  and 


FIG.  394 


INDUCED  CURRENTS  AND   THE   DYNAMO      397 


FIG.  395 


second  fingers  of  the  right  hand  in  such  a  way  that  each 
shall  be  perpendicular  to  the  direction  of  the  other  two ; 
turn  the  hand  so  that  the  thumb  shall  g 

point  in  the  direction  of  the  motion,  and 
the  first  finger  in  the  direction  of  the  lines  Unesqfl 
of  force ;  then  the  second  finger  will  point  * 
in  the  direction  in  which  the  induced  cur- 
rent flows. 

The  rate  at  which  the  lines  of  force 
are  cut  determines  the  induced  E.  M.  F.,  1  volt  being  in- 
duced in  a  conductor  when  it  cuts  100,000,000  lines  of  force 
(maxwells)  per  second. 

Since  lines  of  force  are  closed  circuits,  it  is  sometimes  convenient 
to  consider  a  coil  of  wire  and  these  lines  of  force  as  being  linked  with 
each. other.  In  this  case  the  induced  E.  M.  F.  is  directly  propor- 
tional to  the  rate  of  change  in  the  number  of  linkages. 

(6)  When  the  Magnet  is  Moved.  —  Demonstration.  —  Couple 
a  coil  of  small  insulated  wire,  called  a  secondary  coil,  to  a  sensitive 

galvanometer.  Thrust  the  + 
end  of  a  long  bar  magnet  into 
the  coil  as  shown  in  Fig.  396, 
and  observe  the  throw  of  the 
needle.  Pull  the  +  end  out 
suddenly  and  compare  the 
throw  with  that  obtained  at 
first.  Repeat  both  experi- 
ments with  the  —  end  of  the 
magnet. 


FIG.  396 


This  demonstration, 
compared  with  the  pre- 
ceding, shows  that  it  makes  no  difference  whether  the  coil 
or  the  magnet  is  moved.  A  current  is  induced  whenever 
magnetic  lines  of  force  are  cut  by  a  conductor. 


398  ELECTRICITY 

441.  Primary  and  Secondary  Coils.— Demonstrations.— Select 
a  coil  of  large  wire,  called  a  primary  coil,  of  such  a  size  that  it  will 
easily  go  inside  the  secondary,  and  connect  it  with  a  battery. 

Thrust  it  into  the  secondary 
coil  as  you  did  the  bar  mag- 
net in  the  last  demonstra- 
tion, and  the  same  results 
will  be  obtained.  Why? 

Place  the  primary  coil  in- 
side the  secondary  and  intro- 
duce a  switch  between  the 

FIG.  397  primary    and    the    battery. 

Make  the  circuit  and  notice 

the  deflection.  Break  the  circuit  and  again  notice  the  deflection. 
Compare  the  directions  of  these  deflections  with  those  obtained  in  the 
above  demonstration  by  moving  the  primary. 

Vary  the  demonstration  by  introducing  a  resistance  box  between 
the  primary  coil  and  its  battery,  instead  of  the  switch.  When  a 
steady  current  is  allowed  to  pass,  there  will  be  no  deflection  of  the 
galvanometer.  If  the  amount  of  current  in  the  primary  is  changed, 
however,  either  increased  or  diminished,  the  throw  of  the  needle 
will  show  the  existence  of  an  induced  current. 

Experiment  has  shown  that  the  following  laws  hold  true 
for  induced  currents : 

I.  Whenever  the  current  in  the  primary  coil  is  either  made 
or  increased,  there  is  induced  in  the  secondary  a  current  in  the 
opposite  direction. 

II.  Whenever  the  current  in  the  primary  coil  is  either  broken 
or  diminished,  there  is  induced  in  the  secondary  a  current  in 
the  same  direction. 

442.  Self-induction.  —  We  have  just  seen  that  a  change 
in  the  current  in  one  coil  induces  a  current  in  a  second  coil 
near  the  first.     It  is  evident  that  a  change  of  current  in  one 
turn  of  a  coil  should  also  induce  currents  in  adjacent  turns 


INDUCED  CURRENTS  AND  THE  DYNAMO    399 

of  the  same  coil.     This  effect  is  called  self-indiwtion,  and  its 
existence  can  be  shown  as  follows : 

Demonstration.  —  Couple  a  battery,  switch,  galvanometer,  and 
coil  as  shown  in  Fig.  398.  Turn  on  the  current,  and  observe  the 
direction  of  the  deflection.  Bring  the  needle  back  to  zero,  and  keep 
it  there  by  placing  a  cork  at 
one  side  to  stop  it.  Break  the 
current,  and  notice  that  there 

is  a  throw  of  the  galvanometer  A 

in  the  opposite  direction, 
showing  that  the  current  in- 
duced in  the  coil  is  in  the  same 
direction  as  the  current  sent 
by  the  battery.  FIG.  398 

Let  Fig.  399  represent  five  turns  of  wire  surrounding  an 
iron  core,  carrying  current  away  from  the  observer  in  1,  2, 
3,  4,  5,  and  toward  the  observer  in  1',  2',  3',  4',  5',  as  indi- 
cated. To  understand  the  reason  for  self-induction  let  us 
assume  that  the  current  is  just  beginning,  and  is  increasing 
in  intensity.  Let  us  consider  the  effect  of  the  lines  of  force 
set  up  around  turn  No.  3  by  the  current  passing  through  it. 
As  the  current  increases  in  strength  the  lines  of  force  ex- 
pand from  wire  No.  3  as  a  center,  and  pass  through  the  iron 
core  and  around  the  outside  of  the  wire.  As  they  increase 
in  diameter  they  cut  across  conductors  2  and  1  to  the  left, 
tJL. .?...  *  s  and  across  conductors  4  and  5  to*~ 

— ,  the  right.     By  applying  the  rule  for  •"' 
i  the   direction    of    induced   currents 


(§  440),  we  see  that  in  all  these  con- 
FIG.  399  ductors  the  induced  current  is  in  a 

direction  opposite  to  the  current  already  passing  in  the  coil. 
When  the  current  in  the  coil  is  broken,  the  lines  of  force 
contract  to  the  conductor  that  produced  them;  they  cut 


400  ELECTRICITY 

the  other  turns  in  the  opposite  direction,  so  the  induced  cur- 
rent is  reversed  and  in  the  same  direction  as  the  current  in 
the  coil.  The  same  reasoning  applies  to  every  turn  of  the 


FIG.  400.  —  Ruhmkorff  Coil  connected  with  Cell 

coil.  This  means  that  when  the  current  is  broken,  the  lines 
of  force  belonging  to  every  turn  of  the  coil  cut  every  other 
turn  in  the  coil,  and  the  result  is  a  self-induced  current  of 
considerable  strength. 

443.  The  Induction  Coil,  or  Ruhmkorff  coil,  is  a  combina- 
tion of  coils  used  for  the  purpose  of  getting  induced  currents 
of  high  potential  difference.  Figure  401  is  a  diagram  showing 
the  relation  of  the  parts  in  an  induction  coil.  The  essential 
parts  are  a  soft-  iron  core,  a  primary  coil  of  large  insulated 
wire  connected  with  the  battery,  a  secondary  coil  of  a  very 
much  larger  number  of  turns  of  fine  insulated  wire  con- 
nected with  binding  posts  A  and  B,  an  automatic  make-and- 
break  arrangement  at  P,  between  the  primary  coil  and  the 
battery,  a  condenser  C  connected  with  the  primary  circuit 
on  each  side  of  P,  and  a  switch  S. 

The  operation  of  the  coil  is  as  follows :  When  the  switch 
is  turned  on,  the  current  passes  through  the  primary  and 


INDUCED   CURRENTS  AND   THE   DYNAMO       401 


makes  a  magnet  of  the  iron  core.  This  attracts  the  soft 
iron  armature,  which  is  fastened  to  a  light  spring,  and  breaks 
the  current  at  P.  As  soon  as  this  is  done,  the  core  is  no 
longer  a  magnet,  the  armature  is  thrown  back  by  the  spring, 
the  contact  is  again  made  at  P,  and  the  action  is  repeated. 
When  the  current  is  made  in  the  primary  coil,  a  current  in 
the  opposite  direction  is  induced  in  the  secondary,  and  when 
the  current  in  the  primary  is  broken  there  is  an  induced 
current  in  the  same  direction  in  the  secondary.  The  self- 
induction  of  the  primary  when  the  current  is  made  acts 
against  the  battery 
current  flowing  in  it, 
and  reduces  the  in- 
duced E.M.F.in  the 
secondary;  but  when 
the  current  is  broken, 
the  self-induction 
acts  with  the  battery 
current  and  increases 
the  E.  M.  F.  of  the 
secondary.  The  ef- 
fect of  the  condenser 
is  to  increase  the  ca- 
pacity of  the  primary  coil  and  to  shorten  the  time  of  break- 
ing, thus  raising  the  E.  M.  F.  of  the  secondary.  It  also 
discharges  through  the  battery,  immediately  after  the  cur- 
rent is  broken,  in  a  direction  contrary  to  the  battery 
current ;  this  helps  to  demagnetize  the  core  quickly.  Since 
the  current  in  the  primary  drops  from  a  maximum  to  zero 
much  faster  than  it  rises  from  zero  to  maximum,  the  in- 
duced E.  M.  F.  in  the  secondary  is  correspondingly  higher 
at  the  break  than  at  the  make. 

Rev. 


FIG.  401 


402  ELECTRICITY 

,  The  induced  current  is  of  high  voltage  because  the  total  number 
of  cuttings  of  the  lines  of  force  (§  440)  is  made  very  great  —  in  two 
ways :  the  lines  of  force  of  the  primary  coil  are  increased  in  number 
by  the  presence  of  the  iron  core ;  and  the  secondary  coil  is  made  up 
of  a  very  large  number  of  turns  of  fine  wire,  thus  increasing  the 
number  of  times  that  each  line  of  force  is  cut. 

Since  the  E.  M.  F.  rises  so  high  in  an  induction  coil  the  insulation 
should  be  as  nearly  perfect  as  possible.  In  modern  coils  the  secon- 
dary is  wound  in  sections,  and  these  thoroughly  coated  with  insulat- 
ing wax  under  conditions  that  secure  the  removal  of  all  air. 

444.  Effects  of  the  Inductive  Discharge.  —  The  mechanical 
and  heating  effects  of  the  inductive  discharge  are  practically 
similar  to  those  obtained  from  the  discharge  of  the  Holtz 
or  Wimshurst  machine,  and  the  experiments  made  with  the 
machine  may  be  repeated  and  added  to,  using  the  induction 
coil  instead.  The  physiological  effects  are  peculiar.  They 
should  be  obtained  by  taking  hold  of  the  terminals  of  the 

secondary,  in  a  small  coil.     The  effect  from  a 

large  coil  is  often  painful. 

445.  Luminous  Effects.  —  The  difference  of 
potential  necessary  to  give  a  spark  1  cm.  long 
across  an  air  gap  between  two  parallel  plates 
Js  given  by  Lord  Kelvin  as  30,000  volts.  If, 
however,  the  terminals  are  separated  by  air  at 
a  reduced  pressure,  the  spark  loses  its  intense 
brilliancy,  and  may  be  increased  in  length. 
This  condition  is  secured  by  sealing  platinum 
wires  (§  278)  into  the  opposite  ends  of  a  glass 
FIG.  402  tube  (Fig.  402)  from  which  nearly  all  the  air 
has  been  removed.  When  this  tube  is  attached  to  the  sec- 
ondary terminals  of  a  Ruhmkorff  coil,  in  a  dark  room,  and 
the  current  is  turned  on,  the  tube  will  be  filled  with  a  band 
of  violet  light. 


INDUCED  CURRENTS  AND  THE   DYNAMO      403 

Geissler  Tubes  (Fig.  403)  are  glass  tubes  of  various  forms,  supplied 
with  platinum  terminals  and  filled  with  different  gases  at  different 
pressures.  When  placed  in  the  current  from  the  secondary  of  an 
induction  coil,  they  give  out 
many  brilliant  luminous  ef- 
fects. Commercial  applica- 
tion of  the  light  from  a 
vacuum  .tube  is  made  in  the 
mercury  are  lamp,  in  which 
the  arc  is  carried  by  mercury 
vapor  in  a  state  of  incandes- 
cence. 

The  spark  from  an  induction  coil  can  be  used  to  show  the  conduc- 
tivity of  glass.  If  a  piece  of  small  glass  tubing  is  drawn  down  to  an 
internal  diameter  of  about  1  mm.,  and  then  slipped  over  the  terminals 


FIG.  404 

of  the  coil  (Fig.  404),  a  spark  can  be  sent  through  the  tube.  This 
heats  the  tube,  and  after  a  time  the  spark  goes  from  the  terminals  to 
the  glass,  which  conducts  the  current.  If  this  is  continued,  the  heat 
finally  melts  the  glass. 

446.  The  Dynamo  is  a  machine  for  the  production  of  an 
electric  current  by  the  use  of  mechanical  force.     We  have 
seen  that  whenever  the  lines  of  magnetic  force  are  cut  by 
a  conductor,  a  galvanometer  coupled  to  the  ends  of  the 
conductor  shows  the  presence  of  an  electric  current.     In 
a  dynamo  there  must  be  a  magnetic  field  to  furnish  the  lines 
of  force,  conductors  in  which  the  induction  takes  place,  and 
a  means  of  moving  the  conductors  across  the  lines  of  force. 
This  motion  sets  up  an  electromotive  force  at  the  ends  of 
the  conductors,  and  by  coupling  these  ends  to  an  external 
circuit  a  current  is  obtained. 

447.  The  Ideal  Simple  Dynamo.  —  Under  ideal  conditions 
for  a  simple  dynamo,  the  conductors  would  move  in  a  uni- 


404 


ELECTRICITY 


form  magnetic  field.  The  nearest  approach  to  this  condi- 
tion is  obtained  by  using  permanent  magnets  for  the  fields 

N  and  S,  Fig.  405 ;  a 
machine  of  this  kind 
is  called  a  magneto. 
By  applying  the  laws 
for  induced  currents 
we  may  determine  the 
direction  of  the  cur- 
rent produced  by  the 
dynamo.  Suppose 

the  single  coil  in  Fig.  405  is  turned  from  its  vertical  posi- 
tion, clockwise.  At  the  beginning  of  the  movement,  the 
motion  of  the  conductor  is  almost  parallel  to  the  lines  of  force 
so  that  there  will  be  little  cutting  of  the  lines,  and  little  in- 
duction ;  but  the  rate  at  which  the  lines  of  force  are  cut  in- 
creases until  the  coil  reaches  the  horizontal  position,  and  then 
decreases,  until,  when  the  conductor  has  passed  through 
180°  and  is  again  vertical,  the  induction  again  becomes  zero. 
As  the  upper  branch  descends,  the  direction  of  the  induced 
current  with  reference  to  a  pers©n  looking  from  N  to  S  will  be 
from  the  left  toward  the  right  as  in  Fig.  394.  The  induction 
in  the  lower  part  of  the  loop,  as  it  rises,  will  be  from  right  to 
left,  and  thus  the  two  currents  will  join  and  flow  in  the  same 
direction.  Every  time  the  coil  passes  through  the  vertical 
position,  the  direction  of  the  current  induced  in  it  changes, 
so  that  there  will  be  two  alternations  of  current  for  every 
revolution. 

448.  The  Commutator.  —  In  order  that  the  current  taken 
from  the  coils  of  a  dynamo  may  be  in  one  direction,  the  ends 
of  the  coils  are  connected  with  copper  terminals  that  revolve 


INDUCED  CURRENTS  AND  THE  DYNAMO   405 


FIG.  406 


with  the  shaft,  and  the  currents  are  taken  off  by  fixed  brushes. 

A  two-part  commutator,  suitable  for  a  single  coil,  is  shown 

in  Fig.  406.     A  study  of  this  figure 

will  show  that  the  brushes  can  be 

placed  in  such  positions  that  the 

change  from  one  commutator  bar 

to  the  other  shall  take  place  just 

as  the  direction  of  the  current  in 

the  coil    changes;    and    for    this 

reason  the  current  in  the  external 

circuit  will  always  be  in  one  direction.     The  commutator 

usually  consists  of  as  many  copper  bars,  or  segments,  as 

there  are  coils  of  commutator  wire.     Figure  407  shows  the 

commutator  ready  to  be  fixed  to  the  dynamo  shaft.  Each 

bar  has  a  radial  projection 
at  one  end  with  a  slit  in  it, 
into  which  two  wires  are 
soldered.  These  wires  are  the 
end  of  one  coil  and  the  be- 
ginning of  the  next.  The 
commutator  bars  are  insu- 
lated from  each  other  by 
mica  strips  and  from  the 
shaft  by  thin  mica  rings. 


FIG.  407.  —  Commutator 


449.  The  Armature.— The 
part  of  the  dynamo  in  which 
the  electromotive  force  is  induced  is  called  the  armature. 
This  is  generally  a  rotating  part,  but  in  certain  types  of  ma- 
chines it  is  stationary,  in  which  case  the  magnetic  field  rotates. 
The  core  of  the  armature  is  made  of  soft  iron  in  order  to  in- 
crease the  number  of  lines  of  force  by  reducing  the  reluctance 


406 


ELECTRICITY 


in  the  magnetic  circuit.     Reluctance  in  a  magnetic  circuit 
corresponds   to   resistance   in   an   electrical   circuit,    except 

that  there  is  no  substance 
through  which  the  lines  of 
force  will  not  pass.  In 
most  armatures  the  con- 
ductors lie  in  slots  cut 
into  the  surface  of  the 
core  parallel  to  the  axis. 


FIG.  408.  —  Core  of  Drum  Armature 


450.  The  Ring  Arma- 
ture consists  of  a  number 
of  coils  of  insulated  wire  wound  upon  a  core  which  has  the 
form  of  a  ring.  Figure  409  shows  a  simple  form  of  ring 
armature.  By  applying  the  rule  for  direction  of  induction, 
we  may  determine  the  brush  with  which  the  +  terminal  is 
connected.  Since  one  half  of  the  whole  number  of  coils 
is  in  series  between  the 
brushes  on  each  side,  it  is 
evident  that  the  E.  M.  F. 
will  be  the  sum  of  the 
E.  M.  F.'s  induced  in  all 
the  coils  on  either  side. 
The  resistance  of  the  ar-  FlG  499 

mature  will  be  one  fourth 

of  the  resistance  of  all  the  wire  upon  it,  since  there  are 
two  parallel  circuits  from  the  +  to  the  -  brush,  each  having 
half  the  wire  upon  the  armature  (Formula  59).  This  form 
of  armature  is  adapted  to  machines  designed  for  high  voltage, 
such  as  those  used  in  arc  lighting. 

451.  The  Drum  Armature  consists  of  conductors  wound 
lengthwise  upon  a  cylinder  of  iron.     The  ends  of  each  coil 


INDUCED  CURRENTS  AND  THE   DYNAMO       407 


are  connected  to  adjacent  commutator  bars.  This  form  is 
used  for  lower  E.  M.  F.  than  the  ring  armature.  If  a  large 
current  is  to  be  taken  from  the  machine,  the  conductors 
are  made  of  copper  bars 
or  rods. 


CBC  c  c 


FIG.  410.  —  General  Form  of  Drum 
Armature 

A,  commutator;    B,  wires;   C,  bands  to  hold 
wires  in  slots 


402.  The  Field  Mag- 
net. —  There  are  several 
methods  employed  to  pro- 
duce the  magnetic  field, 
and  these  determine  the 
classes  to  which  dynamos 
belong. 

The  frame  of  a  dynamo 
may  take  any  one  of  a  number  of  forms.  In  Fig.  411, 
which  shows  the  frame  of  a  two-pole  machine,  the  poles  of 
the  electromagnet  are  marked  N  and  S.  C  and  C'  are  the 
cores  upon  which'  the  magnetizing  coils  are  wound,  and  Y*  is. 

the  yoke,  which 
is  of  iron  or  steel, 
and  forms  a  path 
for  the  lines  of 
force  between 
T"  P^  r  \  J  the  magnet  cores. 

r^T  r\   \~7T  The  core  of  the 

armature  is 
marked  c,  and 
the  air  gap  in 
which  the  lines 
of  force  are  cut 

by  the  conductors  is  in  the  space  between  the  core,  c,  and 

the  face  of  either  pole. 


Field  Circuit 


FIG.  411 


408 


ELECTRICITY 


Dynamos  having  more  than  one  pair  of  poles  are  called 
multipolar.  Those  having  two  pairs  are  four-pole,  those 
with  three  pairs  are  six-pole,  and  so  on.  The  number  of 
poles  is  regulated  by  the  use  to  which  the  machine  is  put. 

453.  The  Separately  Excited  Dynamo  has  a  magnetic  field 
produced  by  a  current  from  some  outside  source  of  elec- 
tricity, such  as  a  battery  (Fig.  411)  or  another  dynamo. 
The  advantage  of  this  arrangement  is  that  this  outside  cur- 
rent may  be  regulated  so  that  it  shall  be  constant,  thus  keep- 
ing the  magnetic  field  constant. 

454.  The  Series  Dynamo  has  a  field  produced  by  a  coil  of 
large  wire,  wound  on  the  field  magnets,  that  is  in  series  with 

the  external  circuit.  Figure  412 
shows  how  the  connection  is 
made  from  the  upper  brush 
around  the  field  magnets,  then 
through  the  external  circuit,  and 
back  to  the  lower  brush.  If 
the  resistance  of  the  external 
circuit  is  increased,  the  current 
decreases,  and  consequently  the 
magnetization  of  the  field  and 
the  E.  M.  F.  of  the  dynamo  are  decreased.  If  the  resistance 
of  the  external  circuit  is  decreased,  both  the  magnetization 
of  the  field  and  the  E.  M.  F.  of  the  dynamo  increase. 

455.  The  Shunt  Dynamo.  —  In  the  very  useful  form  called 
the  shunt  dynamo,  the  wire  wound  on  the  field  magnets  is  a 
long  coil  of  small  wire  coupled  to  both  brushes  as  a  shunt 
to  the  external  circuit.     If  the  resistance  of  the  external 
circuit  increases,  less  current  passes  in  that  circuit,  more 


c 


N 


FIG.  412. — Series  Dynamo 


INDUCED   CURRENTS  AND   THE   DYNAMO       409 


current  passes  through  the  shunt,  and  the  magnetism  of  the 
field  is  increased,  causing  the  E.  M.  F.  of  the  machine  to 
rise..  If  the  resistance  of  the  external  circuit  decreases,  the 
E.  M.  F.  of  the  dynamo  falls. 


1 

1 

,^—  — 

<—  —  - 

^     ^ 

1  

^J.      j 

__«»• 

I 

^^"^^_ 

ZT-N                       "\ 

« 

C  ) 

* 

' 

FIG.  413.  —  Shunt  Dynamo 


FIG.  414.  —  Compound  Dynamo 


456.  The  Compound  Dynamo.  —  Since  the  E.  M.  F.  of  the 
series  dynamo  increases  with  the  current  in  the  external  cir- 
cuit, while  the  E.  M.  F.  of  the  shunt  dynamo  diminishes 
as  the  current  in  the  external  circuit  increases,  it  is  possible 
to  wind  both  a  series  and  a  shunt  coil  on  the  same  field 
magnets,  and  so  to  proportion  them  as  to  keep  the  E.  M.  F. 
practically  constant  at  all  loads.  The  compound  dynamo 
is  wound  in  this  way  and  is 
the  machine  used  for  in- 
candescent lighting. 


TIME 


457.  The  Alternating 
Current.  —  The  electro- 
motive force  generated  in 
the  ideal  simple  dynamo  of 
Fig.  405  goes  through  a 
definite  cycle  of  change,  and  when  the  current  passes  into 
an  external  circuit  it  also  goes  through  a  similar  cycle.  If  time 


FIG.  415 


410 


ELECTRICITY 


is  laid  off  on  the  axis  OX  and  current  on  the  axis  yy',  the 
curved  line  of  Fig.  415  will  represent  the  changes  that  take 
place  in  an  alternating  current  during  the  time  of  a  single 
cycle. 

In  the  first  quarter  of  the  time  the  current  has  increased 
from  zero  to  a  maximum  in  one  direction.  It  then  diminishes 
until  at  the  end  of  one  half  the  time  the  current  is  again  zero. 
Reversal  then  takes  place  and  the  current  rises  to  a  maximum 
in  the  opposite  direction  in  three  fourths  of  the  time  and  at 
the  end  of  the  cycle  the  current  is  again  zero. 

In  the  alternating  current  used  for  lighting  there  are  60 
of  these  cycles  per  second. 

458.  The  Alternator.  —  If  the  coils  of  a  dynamo  are 
coupled  to  copper  rings  instead  of  to  the  bars  of  a  commuta- 
tor, the  current  will 
be  an  alternating  one, 
changing  its  direction 
twice  for  every  rota- 
tion of  each  coil  (Fig. 
416).  By  using  as 
many  pole  pieces  to 
the  field  as  there  are 
coils,  and  by  coupling 
the  coils  properly,  the 
currents  in  all  the 
coils  are  put  in  series, 
giving  an  alternating 
current  of  high  E.  M. 
F.  The  field  magnets 

of  an  alternator  are  usually  magnetized  by  a  current  from 
a  small  direct-current  machine  called  an  exciter.  Figure  417 


INDUCED  CURRENTS  AND  THE  DYNAMO      411 


FIG.  417 


shows  the  exciter  at  the 
right,  belted  to  the  pulley 
on  the  alternator  shaft: 
its  current  is  fed  into  the 
stationary  field  magnets 
supported  by  the  frame. 
The  armature  coils  are 
wound  as  flat  coils  on 
the  surface  of  the  rotat- 
ing core. 

Figure  418  represents 
an  alternator  with  re- 
volving field  magnets 
and  a  stationary  arma- 
ture. In  this  machine 
the  exciter  is  direct  con- 


FIG. 


412 


ELECTRICITY 


nected,  that  is,  run  on  the  alternator  shaft.  The  collector 
rings,  outside  the  commutator  of  the  exciter,  lead  its  current 
to  the  field  of  magnets.  The  armature  wire  is  wound  in 
slots  on  the  inside  of  the  stationary  frame,  and  the  cutting 
of  the  lines  of  force  is  produced  by  the  sweeping  of  the  rotat- 
ing magnetic  field  across  the  stationary  conductors. 

459.  Lenz's  Law.  —  A  person  can  turn  the  armature 
of  a  50-H.-P.  dynamo  with  one  hand  so  long  as  there  is  no 
current  generated  and  nothing  to  overcome  but  the  friction ; 
but  when  the  dynamo  is  being  run  at  full  speed  and  the 
current  is  being  used,  the  work  of  an  engine  is  needed  to  turn 
it ;  the  increase  is  the  work  that  is  required  to  force  the  con- 
ductors, while  they  are  carrying  a  current,  through  the  in- 
visible lines  of  magnetic  force.  This  is  in  accordance  with 
Lenz's  law,  which  can  be  stated  thus :  Whenever  a  current 
is  induced  in  a  conductor  by  passing  it  through  afield  of  force, 

the  direction  of  the  induced  current  is 
such  that  the  lines  of  force  generated 
by  it  around  the  conductor  will  op- 
pose the  motion  that  induces  the 
current. 


460.  The  Electric  Motor.  —  We 
have  learned  that  when  a  wire  is 
carried  through  a  magnetic  field, 
cutting  the  lines  of  force,  a  current 
is  generated  in  the  wire.  The  con- 
verse of  this  is  also  true :  if  a  cur- 
rent is  sent  through  a  wire  that  is 
in  a  magnetic  field,  the  wire  will 
be  set  in  motion  in  a  direction 
contrary  to  that  which  would  have 


FIG.  419 


INDUCED   CURRENTS  AND   THE   DYNAMO      413 


produced  the  current.     In  general  any  dynamo  is  reversible 
and  can  be  used  as  a  motor. 

Demonstration.  —  Support  a  horseshoe  magnet  having  a  strong 
magnetic  field  in  a  horizontal  position  as  shown  in  Fig.  419.  Send  a 
current  through  a  No.  30  copper  wire  that  is  hanging  vertically 
between  the  poles.  As  soon  as  the  current  is  turned  on,  the  wire  will 
move  out  from  between  the  poles^  and  if  the  current  is  strong  enough, 
it  will  swing  around  to  the  outside  of  the  N  pole.  The  reason  for 
the  motion  of  the  wire  is  seen  if  we  apply  the  law 
of  the  mutual  action  of  magnetic  lines  of  force  to 
the  magnetic  field  around  the  wire  when  it  is 
between  the  poles  of  the  magnet.  Let  Fig.  420 
represent  a  horizontal  section  through  the  wire 
and  magnet.  The  direction  of  the  lines  of  force 
will  be  indicated  by  the  arrow  points  for  both 
the  permanent  and  temporary  fields.  On  the 
left  of  the  wire  the  lines  of  force  are  in  the  same  direction  and  the 
repulsion  between  them  pushes  the  movable  wire  to  the  right. 

If  we  apply  the  same  law  to  the  mutual  action  between  the 
two  sets  of  lines  of  force  in  the  air  gap  of  a  motor,  the  cause 
of  the  rotation  of  the  motor  will  be  explained.  Let  Fig.  421 


FIG.  420 


z 


\ 


V 


FIG.  421 

represent  a  single  turn  of  wire  in  the  air  gap.  The  direction 
of  the  lines  of  force  generated  around  the  conductor  by  a 
current  that  is  approaching  the  observer,  as  on  the  right 
side  of  the  figure,  is  counter-clockwise.  The  reaction  be- 
tween these  lines  of  force  and  those  generated  by  the  field 
magnets  will  be  repulsion  above  the  wire,  since  the  lines  of 


414  ELECTRICITY 

force  there  have  the  same  direction,  and  attraction  below  it, 
since  the  lines  of  force  there  have  opposite  directions.  The 
result  is  a  tendency  to  drag  the  wire  downward. 

The  direction  of  the  lines  of  force  around  the  wire  on  the 
left  side  of  the  figure,  in  which  the  current  is  going  away  from 
the  observer,  is  clockwise,  hence  there  is  repulsion  below  the 
wire  and  attraction  above  it.  .The  result  of  this  magnetic 
drag  is  a  clockwise  rotation  of  the  armature. 

461.  The  E.  M.  F.  of  a  Dynamo  depends  upon  three 
things :  speed,  number  of  conductors,  and  number  of  lines 
of  force  cut.  The  relation  in  a  two-pole  dynamo  is  expressed 
by  the  formula  ^CN 

~W' 

in  which  n  is  the  number  of  revolutions  per  second,  C  is 
the  number  of  conductors  on  the  armature,  N  is  the  num- 
ber of  lines  of  force  in  the  magnetic  circuit,  and  108  is  a  con- 
stant necessary  to  reduce  the  product  of  nCN  to  volts. 

The  above  formula  is  also  applicable  to  the  back  electro- 
motive force  of  a  motor.  By  this  is  meant  the  E.  M.  F. 
that  is  generated  in  the  armature  of  the  motor  because  of 
the  armature  wires  cutting  the  lines  of  force  in  its  own  field. 

The  existence  of  this  back  E.  M.  F.  is  shown  by  coupling  a  volt- 
meter to  the  terminals  of  a  motor  and  sending  current  from  a  dynamo 
through  the  motor.  The  first  reading  of  the  voltmeter,  before  the 
motor  starts,  will  be  small  and  will  be  due  to  the  potential  drop 
caused  by  the  resistance  of  the  armature.  As  soon  as  the  motor 
Btarts,  the  reading  of  the  voltmeter  begins  to  increase,  and  when  the 
motor  is  running  at  its  rated  speed,  the  back  E.  M.  F.  is  nearly  as 
great  as  the  E.  M.  F.  of  the  dynamo.  The  voltage  sending  current 
through  the  motor  is  the  difference  between  the  E.  M.  F.  of  the 
dynamo  and  the  back  E.  M.  F.  of  the  motor.  This  means  that  as 
the  speed  of  a  motor  increases  the  current  decreases, 


INDUCED  CURRENTS  AND  THE   DYNAMO      415 


An  electric  motor  should  be  run  from  a  current  source  having  a 
constant  electromotive  force.     From  formula  60  we  find  the  value 


of  n  to  be  n 


1  f)8  Ji1  1  08  W 

which  may  be  written,  speed  = 


CN 


CN 


Since  E  is 


FIG.  422 


constant  and  since  C  is  also  constant,  as  it 
is  the  number  of  conductors  on  the  arma- 
ture, it  follows  that  if  we  wish  to  change 
the  speed,  it  must  be  done  by  changing  N, 
the  number  of  lines  of  magnetic  force  in 
the  field  of  the  motor.  Increasing  the 
number  of  lines  of  force  decreases  the 
speed,  and  decreasing  the  number  of  lines 
of  force  increases  the  speed.  This  means 
that  a  motor  runs  faster  with  a  weak 
magnetic  field. 

This   speed  control  is   obtained  in  a 
shunt  motor  by  putting  a  rheostat  in 
series  with  the    shunt  field  winding   as 
shown  in  Fig.  422.     In  this  way  a  wide  range  of  speed  can  be 
obtained. 

462.  Thermoelectric  Currents.  —  We  have  seen  how  an 
electric  current  is  generated  as  a  result  of  chemical  action  in 
a  cell  or  battery  (§  377).  We  have  studied  also  a  second 
method  of  generating  a  current  by  the  use  of  a  generator  or 
dynamo  (§  447).  A  third  method  is  as  follows: 

Demonstration.  —  Twist  together  the  ends  of  a  small  iron  wire 
and  a  small  copper  wire  and  couple  the  other  ends  to  the  terminals  of 
a  sensitive  galvanometer.  Apply  the  heat  of  a  Bunsen  burner  to 
the  twisted  ends  of  the  wires  and  a  movement  of  the  galvanometer 
needle  will  indicate  an  electric  current.  Let  the  heated  ends  of 
the  wires  cool  and  the  needle  will  return  to  zero.  Hold  a  piece  of 
ice  against  the  twisted  wires  and  the  needle  will  move  in  the  opposite 
direction. 

The  two  wires  as  used  in  this  demonstration  form  a  thermo- 
electric couple.  Such  a  couple  will  generate  an  electric 


416 


ELECTRICITY 


current  as  long  as  the  twisted  ends  of  the  wires  differ  in 
temperature  from  the  ends  coupled  to  the   galvanometer. 
An  extensive  use  of  this  current  is  made  in  the 
thermoelectric  pyrometer,  which  is  valuable  in  va- 
rious industrial  operations. 

When  this  instrument  is  used  for  temperatures 
not  to  exceed  1800°  F.  (982°  C.)  the  wires  are 
made  of  nickel  alloys  and  the  couple  is  called  a 
base  metal  couple.  The  wires  are  welded  together 
at  one  end  and  are  separately  inclosed  in  porce- 
lain insulating  tubes  as  shown  in  Fig.  423.  When 
in  use  they  are  inclosed  in  an  outer  protecting 
tube. 

For  high  temperatures  the  thermo-couple  wires 
are  one  of   platinum  and  the  other  of  platinum 
alloyed  with  ten  per  cent  of  rhodium.     This  form 
can  be  used  for  temperatures  as  high  as  2900°  F. 
FIG.  423     (1593°  C.) .    High  temperature  pyrometers  are  used 
in  measuring  the  temperature  of  furnaces,  through 
the  wall  of  which  they 
are  inserted. 

The  reading  instru- 
ment is  a  form  of  mil- 
livoltmeter  in  which 
the  scale  is  calibrated 
in  degrees  Fahrenheit 
or  Centigrade  as  re- 
quired. This  instru- 
ment with  its  cover, 
removed  to  show  its 
interior  construction 
is  shown  in  Fig.  424.  FIG.  424 


INDUCED   CURRENTS  AND  THE   DYNAMO      417 

Questions 

I.  If  two  wires  of  the  spiral  conductor  in  Fig.  387  are  cut  by  a 
vertical  plane,  the  directions  of  the  magnetic  lines  of  force  are  indi- 
cated by  the  dotted  lines  and  arrowheads  in  Fig.  425.    What  law  of 

magnetism  will  explain  the  action  of  the  spiral  ? 
2.  If  two  parallel  wires  have  currents  going 
in  opposite  directions,  one  set  of  the  lines  of 
force  will  be  reversed  (compared  with  their 
direction  in  Fig.  425)  as  in  Fig.  426.  What 

will  be  the  action  of  the  conductors?    How       *"*"" 
FIG.  425  .    ,  i   •      j  9  FIG.  426 

can  it  be  explained  ? 

3.  In  what  ways  can  you  produce  an  induced  current?    Suppose 
two  coils  with  different  numbers  of  turns  are  used  to  slip  over  the 
magnet  in  Fig.  393 ;  how  will  the  induced  electromotive  forces 
compare  ? 

4.  Explain  the  induced  current  in  the  secondary  of  an  induction 
coil  when  the  current  is  "broken  in  the  primary. 

6.  Examine  Fig.  409  and  show  what  part  of  the  wire  on  the 
armature  is  inductor  wire,  that  is,  has  an  E.  M.  F.  induced  in  it, 
and  what  part  is  merely  a  conductor.  Explain. 

6.  What  would  be  the  effect  of  rotating  this  armature  in  the 
opposite  direction? 

7.  What  is  the  function  of  the  iron  core  of  the  field  magnet? 

8.  What  effect  will  it  have  upon  the  voltage  of  a  shunt  dynamo 
to  break  the  external  circuit  ?     Answer  the  same  question  concerning 
a  series  dynamo. 

9.  In  an  alternating  current  each  change  in  direction  of  the 
current  in  a  conductor  is  called  an  alternation.    A  cycle  includes  a 
current  in  both  directions,  so  that  there  are  two  alternations  per 
cycle.     In  a  2-pole  machine  there  are  two  alternations  per  revolu- 
tion.    How  many  r.  p.  m.  (revolutions  per  minute)  must  there  be 
to  give  25  cycles  per  second  ? 

10.  Suppose  you  wish  to  start  a  shunt  motor  at  the  lowest  possible 
speed,  would  you  have  the  resistance  of  the  rheostat  in  Fig.  422  in 
series  with  the  field  or  not  ? 

II.  Suppose  you  are  running  a  lathe  with  a  shunt  motor  and  the 
handle  of  the  rheostat  is  at  about  the  middle  point.     Would  you  put 
in  more  resistance  or  less  to  increase  the  speed  ? 

Rev. 


418  ELECTRICITY 

>, 

Problems 

1.  How  many  volts  difference  of  potential  will  be  generated  in  a 
wire  if  it  cuts  950,000,000  lines  of  force  per  second? 

2.  If  a  2-pole  direct  current  generator  is  sending  75  amperes 
into  its  external  circuit,  how  many  amperes  is  each  conductor  wire 
carrying? 

3.  Answer  problem  2  for  an  alternating  current  generator. 

4.  How  many  r.  p.  m.  must  a  4-pole  machine  have  to  give  60 
cycles  per  second?     How  many  alternations  per  second  will  such  a 
machine  give  ? 

6.  A  2-pole  dynamo  that  generates  110  volts  has  80  con- 
ductors on  the  armature  and  runs  at  a  speed  of  750  r.  p.  m.  How 
many  lines  of  force  are  in  the  magnetic  circuit  ? 

6.  A  dynamo  gives  110  volts  when  it  has  11,000,000  lines  of  force 
in  its  field.  How  many  must  it  have  to  increase  its  voltage  to  120? 

VI.    COMMERCIAL  APPLICATIONS   OF  ELECTRICITY 

463.  The  Telephone  is  an  instrument  used  for  the  pur- 
pose of  transmitting  speech  to  a  distance.  The  receiver  of 
the  Bell  telephone  is  shown  in  section  in  Fig  427.  M  is 
a  horseshoe  magnet,  around  each  pole  of  which  a  coil  of 
fine  wire  is  fixed.  In  front  of  the  poles 
of  the  magnet  a  thin  disk  of  iron  D  is 
fixed  by  its  edge.  Wires  leading  from 
the  coils  through  the  handle  are  fastened 
to  binding  posts  P.  When  a  current 
of  electricity  passes  through  the  coils,  it  will  change  the 
number  of  lines  of  force  going  out  from  the  poles  of  the 
magnet,  and  either  increase  or  decrease  the  attraction 
the  magnet  has  for  the  disk.  If  at  the  transmitting  end 
of  the  line  a  person  speaks  into  a  similar  instrument,  the 
rarefactions  and  condensations  of  air  produced  by  the  voice 
will  cause  the  disk  to  vibrate,  thus  making  rapid  changes 
in  the  distance  of  the  disk  from  the  end  of  the  magnet,  and 


COMMERCIAL  APPLICATIONS 


419 


FIG.  428 


these  will  induce  currents  in  the  coils.  These  currents  coming 
to  the  receiver  end,  and  passing  through  its  coils,  will  set 
up  similar  vibrations  in  its  iron  disk,  which  will  set  up  rare- 
factions *and  condensations  in  the  air  and  thus  reproduce 
the  original  sounds. 

464.  The   Transmitter.  —  While   the   Bell    receiver   was 
originally  used  as  a  transmitter,  many  more  efficient  forms 
have  been  devised.    Among  these 

is  the  solid-back  transmitter,  shown 
in  cross  section  in  Fig.  428.  The 
principle  upon  which  this  is  made 
is  that  of  the  varying  resistance 
of  granular  carbon  produced  by 
pressure  upon  it.  The  essential 
parts  are  the  mouthpiece  M,  the 
metal  case,  the  aluminum  dia- 
phragm D,  the  front  terminal  F,  the  back  terminal  B,  and 
the  granular  carbon  between  the  terminals.  The  terminals 
are  connected  with  the  primary  of  an  induction  coil  in  series 
with  the  line.  A  condensation  of  the  sound  wave  entering 
the  mouthpiece  causes  the  diaphragm  to  compress  the  carbon 
granules;  this  reduces  the  resistance,  and  the  current  is 
increased.  A  rarefaction  causes  the  diaphragm  to  lessen  the 
pressure  on  the  carbon;  this  increases  the  resistance,  and 
reduces  the  current.  These  variations  in  the  current  respond 
with  marvelous  sensitiveness  to  the  vibrations  of  the  dia- 
phragm and  result  in  corresponding  vibrations  in  the  dia- 
phragm of  the  receiving  instrument,  which  is  coupled  in 
series  with  the  secondary  of  the  coil. 

465.  Telephone  Line  Circuit. — One  of  the  many  ways  in 
which  a  subscriber's  instrument  is  coupled  with  a  telephone 
line  is  shown  in  Fig.  429. 


420 


ELECTRICITY 


When  the  subscriber's  receiver  R  is  on  the  hook  the  current  from 
B  passes  through  an  inductive  resistance  a,  the  line  L',  the  storage 

battery  D,  the  call  bell 
C,  the  line  L,  the  central 
Lamp  station  lamp,  and  the  in- 
ductive resistance  6,  to 
the  other  side  of  the  bat- 
tery B.  Since  the  re- 
sistance of  the  call  bell 
is  about  1000  ohms,  the 
current  is  not  enough  to 
light  the  lamp.  When, 

however,  the  receiver  is  taken  from  the  hook,  the  secondary  S 
of  the  induction  coil,  and  the  receiver  in  series  with  it,  is  put  in 
parallel  with  the  call  bell.  As  this  parallel  circuit  has  a  resistance 
of  less  than  50  ohms,  the  current  is  sufficient  to  light  the  lamp  at 
central,  signaling  for  the  line.  The  slight  current  passing  from 
B  through  the  storage  cells  at  D  while  the  receiver  is  on  the  hook 
is  sufficient  to  keep  D  fully  charged,  ready  to  send  its  current 
through  the  local  circuit  when  the  receiver  is  off  the  hook.  The 
transmitter  T  is  shown  in  series  with  the  primary  P  of  the  induc- 
tion coil. 

Central  calls  the  subscriber  by  closing  the  jack  and  cutting  out 
the  lamp,  when  the  current  will  be  large  enough  to  ring  the  bell  C. 

466.  Arc  Lighting. — The  simplest  arc  light  is  produced  by 
sending  a  current  of  electricity  from  one  carbon  rod  to  an- 
other across  a  short  air  gap.  To  maintain  the  ordinary  arc  a 
difference  of  potential  of  from  45  to  50  volts  is  required,  and 
this  sends  through  the  arc  a  current  of  from  9  to  10  amperes. 

The  +  carbon  is  very  much  hotter  than  the  —  carbon, 
and  as  the  current  passes,  the  carbon  becomes  incandescent 
and  some  of  it  crosses  the  space  between,  forming  a  con- 
ductor for  the  current.  This  gives  to  the  +  carbon  a  cup- 
like  shape  in  the  middle,  and  this  cup  is  the  seat  of  the  most 
intense  artificial  light  and  heat  that  have  been  produced. 


COMMERCIAL  APPLICATIONS 


421 


A  type  of  lamp  much  used  in  projection  lanterns  is  the  90° 
angle  lamp,  one  form  of  which  is  shown  in  Fig.  430.  When 
used  with  the  direct  current  the 
horizontal  carbon  is  made  the 
positive  pole  and  its  crater  is 
kept  in  the  axis  of  the  lantern. 
The 'positive  carbon  wears  away 
twice  as  fast  as  the  negative, 
but  both  carbons  can  be  kept 
in  place  as  they  wear  away  by 
being  pushed  forward  by  sepa- 
rate feeding  screws.  This  form 
of  lamp  can  also  be  used  with  the 
alternating  current,  in  which  case 
they  are  fed  at  an  equal  rate. 


FIG.  430 


FIG.  431 


467.  The  Inclosed  Arc  Lamp  has  a  small  globe  nearly 
air-tight  surrounding  the  arc  and  a  few  inches  of  the  carbon. 
In  this  form  of  lamp  the  carbon  is  burned  much  more  slowly 
than  in  the  open  arc,  since  the  supply  of  air  is  cut  off  by 
the  globe.  Figure  431  is  a  diagram  of  the  connections  of 


422  ELECTRICITY 

a  direct  current,  series  multiple  arc  lamp.  The  fall  of  poten- 
tial across  the  arc  is  between  80  and  90  volts.  A  resistance 
is  coupled  in  series  with  the  arc  so  that  the  lamp  can  be  used 
on  a  110- volt  circuit.  There  are  two  electromagnets  that 
control  the  length  of  the  arc.  One  is  a  series  coil  that 
lengthens  the  arc,  and  the  other  is  a  shunt  coil  that  shortens  it. 

468.  The  Luminous  Arc.  —  The  ordinary  carbon  arc  itself 
is  not  luminous,  the  light  coming  from  the  hot  crater  of 
the  positive  carbon.     If,  however,  carbons  are  used  which 
have  a  core  made  of  a  mixture  of  carbon  and  some  metallic 
salts,  the  hot  vapors  given  off  by  these  salts  become  lumi- 
nous when  heated  by  the  current.     If  calcium  salts  are  used, 
.the  color  is  a  golden  yellow,  and  this  arc  is  sometimes  called 
the  flaming  arc,  from  its  resemblance  to  a  flame.     The  arc 
formed  is  much  longer  than  the  ordinary  carbon  arc  and  the 
light  is  exceedingly  brilliant. 

Another  exceedingly  brilliant  source  of  light  is  the  mag- 
netite arc.  This  has  a  heavy  copper  rod  for  the  positive 
upper  terminal  and  a  tube  of  sheet  iron,  packed  with  the 
mineral  magnetite  for  the  lower.  The  terminals  wear  away 
very  slowly  and  the  lamp  is  of  high  efficiency. 

469.  The  Mercury  Vapor  Lamp.  —  When  a  tube,  having  a 
terminal  at  each  end  and  inclosing  a  small  quantity  of  mercury, 
is  exhausted  of  air,  the  mercury  vapor  in  the  tube  will  carry 
the  current  when  it  is  once  started  and  it  will  become  a  source 
of  light.     In  the  Cooper-Hewitt  lamp,  Fig.  432,  the  mercury 
is  held  in  the  large  bulb  at  one  end  of  the  tube  and  serves  as 
the  cathode.     The  anode  is  a  small  iron  cup  at  the  other 
end  of  the  tube.     Platinum  wires  sealed  in  the  glass  carry 
the  current  to  the  electrodes. 

In  the  simplest  form  of  the  lamp  the  tube  is  tilted  by  pulling 


COMMERCIAL  APPLICATIONS 


423 


on  the  suspended  chain  until  the  mercury  rims  through  the 
tube  in  a'  thin  stream.  This  mercury  connects  the  electrodes 
and  starts  the  cur- 
rent. As  soon  as 
there  is  a  break  in 
the  stream,  an  arc  is 
formed,  the  mercury 
vapor  fills  the  tube 
and  sustains  the  arc 
the  full  length  of  the 
tube  when  the  mer- 
cury runs  back. 

The  quality  of  the  light  is  peculiar  in  that  it  contains  no 
red  rays.  In  uses  in  which  the  red  rays  are  required,  as  in 
the  judgment  of  colors,  the  lamp  is  supplied  with  a  trans- 
forming reflector  which  converts  a  portion  of  the  violet  rays 

into  red  and  improves  the  quality  of  the  light 

for  such  purposes. 

470.  Incandescent    Lighting. — When  a 
heavy  current  is  sent  through  a  small  copper 
wire,  the  copper  melts.     If  the  same  experi- 
ment is  made  with  a  platinum  wire,  the  wire 
will  not  melt,  but  will  become  intensely  hot, 
and  glow  with  a  very  bright  light.     Similar 
incandescence  can  be  produced  also  in  some 
other    substances.      The    incandescent    lamp 
(Fig.  433)  consists  of  a  glass  bulb,  into  the 
base  of  which  there  are  sealed  two  platinum 
wires  which  carry  a  loop  of  carbon  filament.     The  air  is 
exhausted  from  the  bulb  before  it  is  sealed.     After  the  lamp 
is  screwed  into  the  base  there  is  but  one  gap,  in  the  circuit 


FIG.  433 


COMMERCIAL  APPLICATIONS  425 

at  G.  This  is  closed  when  the  lamp  is  turned  on.  When 
the  proper  current  is  sent  through  the  carbon  filament,  it 
becomes  incandescent,  but  does  not  burn,  as  there  is  no  air 
in  the  bulb.  After  a  lamp  has  been  used  for  some  time, 
part  of  the  carbon  becomes  deposited  on  the  inside  of  the 
bulb,  and  absorbs  a  great  deal  of  the  light  sent  out  by 
the  filament.  When  this  has  happened,  the  best  economy 
is  to  replace  the  lamp  with  a  new  one. 

471.  Metallized  Filaments.  —  If  the  carbon  filament  is 
"  metallized  "  by  subjecting  it  to  the  intense  heat  of  an 
electric  furnace,  it  is  rendered  much  more  refractory,  that 
is,  capable  of  being  brought  to  a  higher  temperature  with- 
out melting.      The   higher   temperature  causes  the  metal- 
lized filament  to  gi.ve  out  more  light  than  the  ordinary 
carbon  filament  for  the  same  expenditure  of  electrical  energy. 
A  carbon  lamp  gives  16  candle  power  for  about  50  watts, 
requiring  3.1  watts  per  candle  power.     The  metallized  fila- 
ment lamp  gives  about  20  candle  power  for  50  watts,  or  2.5 
watts  per  candle  power. 

472.  True  Metal  Filament  Lamps  of  high  efficiency  have 
also  been  developed.    These  lamps  depend  upon  the  possibil- 
ity of  drawing  certain  of  the  less  common  metals,  like  tanta- 
lum and  tungsten,  into  a  flexible  wire  of  very 

small  diameter —  0.1  mm.  or  less  —  and  also  upon 
the  ability  of  these  wires  to  carry  a  current  that 
brings  them   to   incandescence  without   bringing 
them  to  the  melting  point.     The  tungsten  lamp 
(Fig.  435)  is  of  much  higher  efficiency  .than  the 
carbon  or  metallized  filament  lamp.     A  40-watt     FlG- 435 
tungsten  lamp  will  give  32  candle  power  or  more,  requiring 
less  than  1.25  watts  per  candle  power.     This  is  most  im- 


426 


ELECTRICITY 


D 


K 


FIG.  436 


portant  to  the  consumer,  because  what  he  pays  for  is  watt 
hours  and  what  he  wishes  to  use  is  light,  hence  a  tungsten 
— ..  gives  him  twice  the  returns  that  a  metal- 

_l_  <y\"//<?~~     lized  filament  lamp  gives. 

473.  The  Incandescent  Circuit.  —  Incan- 
descent lamps  are  coupled  in  parallel  across 
the  mains,  or  wires  leading  from  the  dy- 
namo. Figure  436  illustrates  a  simple  in- 
candescent circuit.  The  dynamo  D  is  first 
run  until  its  voltage  is  110  volts,  and  then 
any  lamp  or  group  of  lamps  in  the  circuit 
can  be  turned  on.  The  hot  resistance  of 
a  110-volt,  16-candle-power  lamp  is  about  220  ohms;  con- 
sequently each  lamp  requires  a  current  of  half  an  ampere. 
The  parallel  resistance  of  2,  3,  or  n  lamps  being  only  J, 
J,  ^th  part  of  the  resistance  of  a  single  lamp, 
the  same  dynamo  that  will  light  one  lamp 
will  light  a  number.  If  it  were  possible  to  build 
a  dynamo  without  any  internal  resistance,  the 
number  of  lamps  that  could 
be  lighted  would  be  very 
large.  As  this  cannot  be 
done,  the  number  is  limited. 
Several  groups  of  wires  are 
usually  run  from  one  dy- 
namo. A  group  can  be  run 
from  the  mains  at  any  point 
by  coupling  submains  to  them,  that  is,  by  attaching  to  each 
wire  a  branch  wire  large  enough  to  carry  the  current  for  its' 
group  (Fig.  437).  It  is  customary  to  put  a  fuse  (Fig.  339) 
between  each' branch  circuit  and  the  main. 


FIG.  437.  — Branch  Circuits 


Each  arch  in  the  line  where  one 
conductor  crosses  another  indi- 
cates that  the  two  do  not  touch, 
or  that  they  are  insulated  from 
each  other. 


COMMERCIAL  APPLICATIONS  427 

474.  The  Three-wire  System.  —  In  order  to  reduce  the 
expense  of  distribution,  Edison  devised  the  three-wire  sys- 
tem, in  which  two  simi- 

lar dynamos  D,  D'  are  ---  ,  _  ,__^_^__^ 
coupled  in  series  (Fig.  \  y  T  i  .  T  * 
438)  .  The  main  feeding  ~  ~ 

wires  are  attached  one 


,1  ...  »     ,,       FIG.  438.  —  Three-wire  System  \ 

to  the  positive  of  the 
first  dynamo,  and  the  other  to  the  negative  of  the  second. 
A  third  wire  is  attached  to  the  negative  of  the  first  and 
to  the  positive  of  the  second  dynamo.  If  there  are  equal 
numbers  of  lamps  burning  on  both  sides  of  the  middle 
wire,  it  will  carry  no  current,  but  if  there  are  50  lamps  on 
one  side  and  55  on  the  other,  for  instance,  it  will  carry  the 
current  for  5  lamps.  The  middle  or  neutral  wire  is  often 
grounded. 

475.  Alternating  Current  Transformer.  —  Since  alternat- 
ing dynamos  are  built  to  give  high  voltage,  some  method 
is  necessary  for  changing  this  voltage  to  that  which  can  be 
used  in  a  lamp.  A  step-down  transformer  is  used  for  this 
purpose  ;  it  is  virtually  a  reversed  Ruhmkorff  coil,  —  re- 
versed because  the  work  to  be  done  is  to  change  a  high  poten- 
tial current  into  one  of  a  low  potential.  The  principle  of  the 
step-down  transformer  is  shown  in  Fig.  439.  The  current 

from  the  dynamo  flows  through 
a  long  coil  of  fine  wire  which 
has  an  iron  core  to  increase  the 
magnetic  field.  Surrounding 
the  same  core  is  a  second  coil, 

shorter  and  of  larger  wire.     To  the  terminals  of  this  coil 
are  attached  the  lamps  to  be  lighted.     The  proper  size  and 


428 


ELECTRICITY 


length  of  the  wire  in  each  coil  are  determined  by  the  re- 
spective voltages  of  -the  dynamo  and  of  the  lamps  to  be 

used.  A  step-down  trans- 
former reduces  the  voltage  in 
the  same  ratio  as  that  of  the 
numbers  of  turns  in  the  two 
coils.  For  instance,  to  re- 
duce a  1000- volt  current  to 
one  of  100  volts,  the  number 
of  turns  in  the  primary  must 
be  10  times  the  number  in 
the  secondary.  Very  little 
energy  is  lost  in  the  trans- 
formation ;  if  the  1000- volt 
current  sent  into  the  trans- 
former is  of  1  ampere,  the  100- 
volt  current  taken  from  it  will  be  of  very  nearly  10  amperes. 


FIG.  440 


Figure  440  shows  in  cross  section  the  details  of  a  step-down  trans- 
former with  the  relation  of  its  parts,  P  being  the  windings  of 
the  primary  coil  and  S  of  the  secondary; 
and  Fig.  441  shows  the  instrument  as  set 
up  for  use.  This  is  the  kind  used  on  a  line 
pole  to  reduce  the  1000- volt  current  from 
the  station  to  a  lower  voltage  current  for 
house  use.  When  in  use,  it  is  filled  with  oil 
for  insulation. 

A  step-up  transformer  changes  a  current 
of  low  voltage  to  one  of  high  voltage ;  it 
has  a  greater  number  of  turns  in  the  sec- 
ondary than  in  the  primary.  FIG.  441 

476.  Electric  Railways.  —  The  trolley  lines  and  third-rail 
railways  of  the  United  States  have  for  their  essential  parts 


COMMERCIAL  APPLICATIONS 


429 


the  generating  stations  and  generators,  feed  wires,  trolley 
wires  or  third  rails,  the  cars,  and  the  road  bed.  The  genera- 
tors are  usually  direct-current  dynamos  producing  current 

Weed  Hire 


Trrtll&u  ftirf! 


) 

'DDQDD 

I] 

DDDDD 

II 

o 

Hail 

FIG.  442 

at  a  pressure  of  about  500  volts.  The  positive  poles  of  these 
dynamos  are  connected  to  the  feed  wires,  trolley  wires,  or 
third  rails,  while  the  negative  poles  are  connected  to  the  rails, 
which  serve  as  return 
conductors. 

Feed  wires  are  used 
when  the  line  is  a  long 
one  ;  they  are  connected 
to  different  sections  of 
the  trolley  wire.  The 
current  goes  from  the 
trolley  wire  to  the  wheel 
in  contact  with  it,  down 
the  conductor  carried  by 
the  pole,  to  the  motor, 
then  through  the  car 
wheels  to  the  track  and 
then  to  the  dynamo.  The  cars  are  in  parallel,  like 
incandescent  lamps  on  a  lighting  circuit,  and  each  takes  its 
own  current,  independent  of  the  rest.  The  amount  of  cur- 
rent taken  by  each  car  depends  largely  upon  the  load  in 
the  car  and  the  grade  of  the  road.  Since  the  motors  are 


FIG.  443.  —Trolley  Car  Motor,  with 
case  opened 


430 


COMMERCIAL   APPLICATIONS  431 

subject  to  the  severest  kind  of  usage,  they  are  protected 
with  water-tight  cases. 

Hundreds  of  electric  railways  transport  people  to  and  from  their 
places  of  business  in  large  cities.  Figure  444  shows  a  transconti- 
nental passenger  train  on  an  electric  railway.  Another  important 
use  of  motors  is  their  application  to  individual  machines  such  as 
printing  presses,  lathes,  band  saws,  etc.  Each  machine  can  then 
be  run  separately  without  large  waste  of  power  through  the  fric- 
tion of  shafts  and  belting. 

477.  The  Transmission  of  Electrical  Energy. —  The  func- 
tion of  a  transmission  line  is  to  transmit  electrical  energy 
to  a  distance.     There  is  always  a  certain  loss  in  transmis- 
sion, due  chiefly  to  the  heating  of  the  line.     As  the  heating 
of  a  conductor  is  proportional  to  the  square  of  the  current, 
it  is  plain  that  the  current  sent  should  be  as  small  as  possible. 
To  transmit  10,000  watts  of  electrical  power  by  using  1 
ampere  at  a  pressure  of  10,000  volts  is  much  more  economical 
than  to  send  10  amperes  at  a  pressure  of  1000  volts.     For  this 
reason  transmission  lines  are  high  tension  lines,  and  require 
only  a  small  wire  to  carry  the  current. 

For  instance,  the  alternators  of  the  electric  road  from  Philadel- 
phia to  Atlantic  City  give  6600  volts,  but  this  current  is  changed  to 
one  of  33,000  volts  by  the  use  of  step-up  transformers.  It  is  sent 
over  the  line  at  this  voltage  to  the  substations  where  the  voltage  is 
reduced  to  430  volts  by  step-down  transformers  and  then  fed  into 
the  alternating  side  of  a  rotary  converter,  from  the  direct  current 
side  of  which  a  direct  current  of  650  volts  is  taken.  This  is  fed  into 
the  third  rail  which  feeds  the  motors  on  the  cars. 

478.  Electric  Welding.  —  The  heating  effect  of  the  cur- 
rent is  used  effectively  in  electric  welding.     For  this  pur- 
pose heavy  currents  are  used,  such  as  are  supplied  from  the 
low-voltage  side  of  a  step-down  transformer.     The  reason 
for  this  may  be  seen  from  a  review  of  section  402. 


432 


ELECTRICITY 


Demonstration.  —  Couple  two  insulated  copper  bell  wires  to  a 
110- volt  circuit  in  series  with  a  110-volt  lamp ;  hold  them  touching 
end  to  end.  The  current  passing  through  the  high  resistance  of  the 
junction  of  the  two  wires  will  produce  so  great  heat  that  the  ends 
will  melt  and  on  being  pushed  together  the  wires  will  become 
welded  and  form  a  single  conductor. 

This  is  an  example  of  what  is  known  as  resistance  welding. 
The  pieces  to  be  welded  are  held  together  end  to  end  and 
when  the  metal  becomes  plastic  the  ends  are  pushed  to- 
gether and  the  current  turned  off.  Special  machines  are 
used  to  perform  these  operations  in  regular  succession. 

Another  type  of  electric  welding,  called  spot  welding,  is 
used  to  weld  one  sheet  of  metal  to  another.  Two  large 
electrodes  are  used  to  press  the  metal  surfaces  together  and 
to  localize  the  heat  of  the  current. 
These  electrodes  are  shown  at  E 
in  Fig.  445.  The  pieces  to  be 
welded  are  placed  between  the 
electrodes  and  on  pulling  down 
the  lever  L  or  pressing  down  the 
treadle  T  the  pressure  is  applied 
and  the  current  turned  on  for  the 
few  seconds  necessary. 

Another  form  of  welding,  called 
seam  welding,  makes  use  of  the 
great  heat  of  the  electric  arc. 


FIG.  445.  —  Spot-welding 
Machine 


Questions 

1.  Make  a  drawing  showing  how  the  lines  of  force  go  through  the 
diaphragm  of  a  telephone  receiver. 

2.  How  do  you  explain  the  heavy  current  that  passes  through 
the  carbons  of  an  arc  lamp  when  the  lamp  is  first  turned  on? 

3.  Why  is  platinum  used  instead  of  copper  for  the  sealing-in 
wire  of  incandescent  lamps? 


COMMERCIAL    APPLICATIONS  433 

4.  Why  is  it  a  good  plan  —  whenever  a  dynamo  supplies  current 
to  a  number  of  groups  of  lamps  —  to  place  a  fuse  between  each  group 
and  the  mains? 

5.  Why  is  it  necessary  to  use  a  step-down  transformer  between 
the  street  mains  of  an  alternating  system  and  the  house  lighting? 

6.  Why  is  it  best  to  use  a  step-up  transformer  between  the  alter- 
nating current  generator  and  the  transmission  line? 

Problems 

1.  A  small  arc  lamp  requires  a  current  of  4  amperes  and  a  dif- 
ference of  potential  at  its  terminals  of  45  volts.     What  is  the  resist- 
ance of  the  lamp?     What  resistance  must  be  put  in  series  with  it 
on  a  110-volt  circuit? 

2.  An  open  arc  requires  a  voltage  of  45  volts  and  a  current  of  9 
amperes.     What  is  the  resistance  of  the  arc?     How  much  resistance 
must  be  put  in  series  with  the  arc  to  burn  it  across  a  110-volt  circuit? 
How  much  must  be  put  in  if  two  arcs  are  put  in  series  across  this 
circuit?     How  much  current  will  they  take? 

3.  The  positive  carbon  of  a  projection  lantern  (§  466)  burns  off  an 
inch  in  length  in  40  minutes.     How  much  will  each  carbon  be 
shortened  if  the  lantern  is  run  for  a  lecture  lasting  an  hour  and  a  half? 

4.  A  projection  arc  lamp  that  takes  10  amperes  at  a  voltage  of 
55  volts,  is  sometimes  run  on  a  220-volt  circuit  for  the  purpose  of 
getting  a  steadier  light.     What  resistance  must  then  be  placed  in 
series  with  it? 

6.  Twelve  open  arc  lamps,  each  requiring  50  volts  and  9.6  am- 
peres, are  coupled  in  series  and  run  by  a  dynamo.  How  many  volts 
must  it  give?  How  many  amperes?  What  is  the  resistance  of  the 
12  lamps  in  series?  What  resistance  must  be  put  in  series  with 
them  to  reduce  the  current  to  9  amperes? 

6.  A  certain  inclosed  arc  lamp  requires  4.5  amperes,  but  the  volt- 
age at  its  terminals  must  be  80  volts  to  run  it  properly.     What  is 
the  resistance  of  the  inclosed  arc  lamp?     How  much  resistance  must 
be  put  in  series  with  it  to  burn  it  across  a  110-volt  circuit? 

7.  What  must  be  the  resistance  of  the  heating  coil  of  a  trolley 
car  so  that  the  current  shall  be  75  amperes  on  a  550-volt  circuit? 
Find  the  number  of  watts. 

Rev. 


434  ELECTRICITY 

8.  The  searchlight  projector  at  Fort  Monroe  has  a  diameter  of 
60  inches.     With  150  amperes  at  60  volts  the  arc  gives  194,000,000 
candle  power.    What  is  the  resistance  of  the  arc?    How  many 
candle  power  does  it  give  per  watt? 

9.  A  D.C.  flaming  arc  lamp  is  run  on  a  115- volt  circuit  and  re- 
quires 6.5  amperes.     The  arc  itself  takes  70  volts.     Find  the  ter- 
minal watts,  the  arc  watts,  the  resistance  of  the  arc,  the  resistance 
in  series  with  the  arc,  and  the  efficiency  of  the  lamp. 

10.  How  much  current  is  required  by  a  40-watt  Mazda  lamp  run 
on  a  110-volt  circuit?     How  much  is  required  by  a  60-watt  lamp  on 
the  same  circuit? 

11.  Suppose  15  of  the  40-watt  lamps  of  problem  10  are  burning 
on  one  side  of  the  neutral  wire  in  a  3-wire  system,  and  12  of  the 
60-watt  lamps  on  the  other  side.     How  much  current  is  the  wire  on 
the  40-watt  side  carrying?     How  much  is  the  wire  on  the  60-watt 
side  carrying?     How  much  does  the  neutral  wire  carry? 

12.  Mazda  B  lamps  for  electric  railway  service  are  run  5  in  series 
on  a  550- volt  circuit.     How  many  volts  does  each  lamp  require? 
How  many  amperes  if  they  are  36-watt  lamps?    What  is  the  re- 
sistance of  each  lamp?    How  much  heat  does  each  lamp  give  to  the 
car  per  minute? 

13.  How  many  amperes  are  required  in  an  electric  furnace  that 
runs  on  a  70-volt  circuit  and  uses  9  kilowatts? 

14.  To  weld  an  average  sized  rail  bond  to  a  rail  requires  2000 
amperes  at  5  volts.     Find  the  resistance  of  the  joint.    How  many 
calories  per  minute  are  developed? 

15.  A  1000-volt  current  of  3  amperes  is  sent  through  the  primary 
of  a  transformer  having  an  efficiency  of  97  per  cent.     How  many 
104- volt  lamps  can  it  light  if  each  requires  0.52  ampere? 

16.  On  the  first  floor  of  a  house  12,  40-watt,  Mazda  (tungsten) 
lamps  are  used.     On  the  second  floor  18,  25-watt,  lamps  of  the 
same  kind  are  used.     How  much  current  will  be  required  to  run  all 
the  lamps  at  the  same  time,  if  they  are  run  on  a  110-volt  circuit? 


CHAPTER   X 

LIGHT 
I.     NATURE  AND  INTENSITY  OF  LIGHT 

479.  Light  is  the  form  of  radiant  energy  which,  by  its 
effect  upon  the  retina,  excites  the  sensation  of  vision. 
There  are  many  reasons  for  supposing  that  this  action  is 
a  vibration  of  the  ether  (§§  271,  272).  This  vibration,  un- 
like sound  vibration,  is  transverse,  —  that  is,  perpendicular 
to  the  direction  in  which  the  light  is  moving. 

Luminous  bodies  are  those  that  emit  light.  The  term 
is  usually  applied  to  those  bodies  only  that  are  self- 
luminous.  When  light  falls  upon  a  body,  part  of  it  is  re- 
flected ;  part  is  absorbed  by  the  body,  changing  the  molec- 
ular or  atomic  force;  and  part  may  or  may  not  pass 
through  the  body.  Transparent  bodies  are  those  that  permit 
light  to  pass  through  them  in  such  a  way  that  objects  are 
distinctly  visible  through  them.  When  light  comes  through 
a  body  as  diffused  light,  and  objects  cannot  be  distinctly 
seen  through  it,  the  body  is  called  translucent.  If  the  body 
does  not  permit  light  to  pass  through  at  all,  it  is  called  an 
opaque  body. 

The  classification  of  bodies  as  opaque  and  transparent 
is  not  very  accurate,  for  thick  layers  of  transparent  bodies 
absorb  a  great  deal  of  light,  while  thin  layers  of  opaque 
substances  are  sometimes  transparent. 

435 


436  LIGHT 

Demonstration.  —  The  transparency  of  gold  leaf  can  readily  be 
shown  by  laying  a  piece  of  gold  leaf  upon  a  glass  plate  and  covering 
it  with  another  plate  of  the  same  size.  It  is  well  to  bind  these 
together  with  a  strip  of  gummed  paper  such  as  is  used  in  making 
lantern  slides.  Hold  the  plates  close  to  the  eye  and  objects  can  be 
seen  clearly  through  the  gold  leaf.  Compare  the  color  of  the  trans- 
mitted light  with  the  color  that  is  reflected  from  gold. 

480.  The  Propagation  of  Light.  —  A  luminous  ray  is  a 
sin'gle  line  of  light  propagated  from  a  luminous  point.  It 
is  always  perpendicular  to  the  front  of  the  advancing  light 
wave,  and  in  the  case  of  a  spherical  wave  is  a  radius  drawn 
from  the  source  of  light.  A  group  of  rays  from  the  same 
source  is  a  pencil  of  rays.  If  these  rays  are  parallel,  they 
constitute  a  beam  of  light.  If  they  diverge  from  a  point, 
they  xform  a  diverging  pencil.  If  they  meet  at  a  point,  they 
form  a  converging  pencil. 

In  a  homogeneous  medium,  the  direction  of  propagation  of 
light  is  in  straight  lines.  But  light  is  affected  by  gravita- 
tion ;  thus  when  the  ray  from  a  star  passes  near  the  sun  it 
is  bent  slightly  towards  the  sun  out  of  its  straight-line 
path,  to  the  extent  predicted  by  Einstein. 

481.  Umbra  and  Penumbra. — Demonstration. — Select  a 
board  about  2  ft.  long  and  8  in.  wide,  and  set  up  in  the  middle  of 

it  a  wooden  cylinder  2  in.  in  diam- 
eter and  5  in.  high.  Fasten  an  up- 
right 6  in.  high  to  one  end  of  the 
board  and  near  the  other  end  set  up 
two  candles  4  in.  apart.  Observe 
the  shadows  cast  by  the  cylinder 
FIG.  446  upon  the  upright. 

The  dark  part  where  the  shadows  overlap  is  the  umbra, 
and  the  part  which  is  lighted  by  only  one  candle  is  the  pe- 
numbra. When  a  single  source  of  light  is  so  small  as  to 


NATURE  AND  INTENSITY  OP  LIGHT 


437 


be  considered  a  point,  the  shadow  is  all  umbra.  If  the  source 
of  the  light  is  larger,  the  umbra  is  partly  or  completely  sur- 
rounded by  a  penumbra.  Figure  447  illustrates  the  case  in 
which  the  light  comes  from  a  luminous  ball  and  the  opaque 
body  is  a  larger  ball.  If  L  is  the  luminous  and  B  the  opaque 
ball,  a  screen  S  will  show  the  existence  of  a  circular  umbra 
or  shadow  whose  limits  can  be  determined  by  moving  a 
straight  line  around  both  balls  and  tangent  to  both  of  them 


FIG.  447 


on  the  same  side,  as  LB.  There  will  be  a  penumbra,  however, 
entirely  around  the  umbra ;  this  will  extend  to  the  limits  of 
a  circle  marked  by  a  line  tangent  to  both  balls,  but  always 
on  opposite  sides  of  them,  as  CB.  At  the  edge  of  the  umbra 
the  penumbra  will  be  nearly  as  dark  as  the  umbra,  and  it 
will  gradually  grow  lighter  and  lighter  toward  the  outer 
edge.  The  moon  is  much  smaller  than  the  sun,  its  diameter 
being  2163  miles,  but  its  distance  from  the  earth  is  so  much 
less,  that  it  appears  to  be  of  nearly  the  same  size.  In  its 
journey  around  the  earth  the  moon  sometimes  comes  be- 
tween us  and  the  sun  and  acts  as  a  screen,  cutting  off  the 
sun's  light  from  us.  If  the  observer  is  at  a  part  of  the 
earth  where  the  light  of  the  sun  is  entirely  cut  off,  as  in  the 


438 


LIGHT 


umbra  of  Fig.  447,  the  eclipse  is  total.  If  he  is  where  a 
portion  of  the  sun  can  be  seen,  he  is  in  the  penumbra  and 
the  eclipse  is  partial,  as  in  Fig.  448. 


FIG.  448 

482.  The  Formation  of  Images.  —  An  image  is  the  pic- 
ture of  an  object  formed  by  rays  of  light  coming  from  it. 
The  image  formed  by  rays  passing  through  a  small  opening 
is  always  inverted.  That  this  must  be  so  is  shown  by  a  study 
of  Fig.  449,  which  illustrates  the  formation  of  an  image  by  a 


FIG.  449 

pinhole  camera.  Since  all  the  light  that  forms  the  image 
comes  through  the  pinhole,  all  the  rays  that  are  not  parallel 
must  cross  in  passing  through  it.  The  ray  coming  from  the 
top  of  the  object  forms  its  image  at  the  bottom.  The  ray 
from  the  bottom  of  the  object  goes  to  the  top  of  the  image. 
The  ray  from  the  right  side  strikes  the  left,  etc.  Hence  there 
is  a  complete  reversal  in  the  image. 


NATURE  AND  INTENSITY  OF  LIGHT  439 

If  a  room  is  darkened  and  sunlight  is  let  into  it  through  the  side 
of  a  Venetian  blind,  a  series  of  sun  images  will  be  formed  on  the  walls 
or  floor  wherever  the  light  falls.  If  sunlight  comes  through  a  dusty 
window  pane  into  a  darkened  room,  the  lighted  part  of  the  wall 
opposite  is  made  up  of  a  number  of  overlapping  images  of  the  sun. 
In  partial  eclipses  of  the  sun,  the  light  coming  through  small  open- 
ings in  the  leaves  of  trees  will  form  inverted  crescent  images  of  the 
sun  on  the  ground. 

483.  The  Velocity  of  Light  was  long  thought  to  be  instan- 
taneous.    In  1675,  however,  Romer,  a  Danish  astronomer, 
determined  the  ve- 

locity  of  light  by 
a  study  of  the  sat- 
ellite  of  Jupiter. 
One  of  the  moons  of  Jupiter,  in  its  path  around  the 
planet,  passes  into  the  shadow  of  the  planet  once  in  42  hr. 
28  min.  and  36  sec.,  on  the  average.  Romer  noticed  that 
while  the  earth  was  passing  from  E  to  Ef  the  observed  times 
of  the  eclipses  were  later  than  the  computed  times,  and  that 
the  differences  between  them  kept  increasing  until,  after 
six  months,  at  Ef,  the  total  retardation  was  16  min.  36  sec. 
This  means  that  it  takes  the  light  16  min.  36  sec.  to  cross 
the  orbit  of  the  earth,  about  196,000,000  miles.  This  gives  a 
velocity  of  about  186,000  miles  or  300,000  km.  per  second. 

The  determination  has  been  made  in  other  ways,  and  the 
results  confirm  Romer's  measurement.  The  velocity  is  so 
great  that  light  could  travel  around  the  earth  nearly  7^  times 
in  1  second. 

484.  The  Intensity  of  Illumination  is  measured  by  the 
quantity  of  light  that  falls  on  a  unit  of  surface.     This  differs 
with  the  intensity  of  the  source  of  the  light,  and  with  the 
distance  from  the  source. 


440 


LIGHT 


The  intensity  of  illumination  upon  any  surface  is  inversely 
proportional  to  the  square  of  its  distance  from  the  source  of 
light.  This  law  is  true  for  very  small  sources  of  light  only. 
It  can  be  verified  as  follows : 

Demonstration.  —  Place  a  lamp  close  to  a  screen  through  which 
there  is  a  small  hole.  At  a  distance  of  1  ft.  place  a  cardboard  disk 


FIG.  451 

1  in.  in  diameter.  Place  a  screen  2  ft.  from  the  light,  and  the 
shadow  cast  by  the  disk  will  be  2  in.  in  diameter,  and  its  area  four 
times  that  of  the  disk.  Since  the  disk  cuts  off  the  light  from  a  part 
of  the  screen  four  times  as  great  as  itself,  the  intensity  of  the  light 
falling  upon  the  screen  must  be  only  one  fourth  as  great  as  that 
falling  upon  the  disk.  If  the  screen  is  placed  three  feet  from  the 
light  the  intensity  will  be  only  one  ninth  as  great. 

485.  Photometry  is  the  process  of  measuring  the  relative 
intensities  of  light.  The  instruments  used  for  the  purpose 
are  called  photometers.  The  practical  working  standard 
of  intensity  is  the  incandescent  lamp.  This  is  first  standard- 
ized in  terms  of  candle  power  based  upon  the  light  given  by 
a  sperm  candle,  and  after  being  "  seasoned  "  by  use  gives  a 
nearly  constant  candle  power.  From  tests  made  at  the 
Bureau  of  Standards  at  Washington  the  average  candle  power 
of  carbon  filament  lamps  with  a  current  of  0.5924  ampere 
was  16.  The  25-watt  tungsten  lamp  gives  20  candle  power 
and  the  Welsbach  mantle  lamp  under  good  gas  pressure,  50 
candle  power  or  more. 


NATURE  AND   INTENSITY   OF  LIGHT 


441 


486.  The  Bunsen  Photometer  consists  of  a  screen  of  un- 
glazed  white  paper  having  in  the  middle  a  spot  of  paraffin 
or  oil.  It  is  sometimes  called  the  grease  spot  photometer. 
Figure  452  shows  the  arrangement  of  the  spot  box  with  two 
mirrors  M  and  Mf  so  inclined  that  the  two  images  of  the  spot 


will  be  seen  side  by  side.  The  sources  of  light  to  be  compared 
are  placed  one  on  each  side  of  the  screen  and  at  such  distances 
that  the  spot  is  invisible.  This  takes  place  when  the  same 
amount  of  light  strikes  upon  each  side  of  the  screen,  from  the 
two  light  sources.  Applying  the  law  of  light  intensity  we 
have  from  Fig.  452 


S:  L= 


hence 


(61) 


487.  The  Joly  Photometer.  —  One  of  the  simplest  pho- 
tometers to  make  is  the  Joly,  which  consists  of  two  square 
pieces  of  paraffin  with  a  piece  of  tin  foil  between  them.  If 
this  is  used  in  place  of  the  spot  box  of  the  Bunsen  photometer, 
the  two  sides  will  be  equally  lighted  and  appear  equally 
bright  when  S  :  L  =  d? :  d'2  as  before. 


442  LIGHT 

Questions 

1.  Would  a  perfectly  transparent  body  be  visible? 

2.  What  do  we  assume  concerning  the  propagation  of  light  when 
we  aim  a  gun  ? 

3.  Show  by  a  figure  the  relative  positions  of  the  sun,  earth,  and 
moon  when  there  is  (a)  a  total  eclipse  of  the  sun ;  (b)  a  partial  eclipse 
of  the  sun ;  (c)  a  total  eclipse  of  the  moon. 

4.  What  shapes  of  shadow  can  a  disk  give  upon  a  screen  ?   What 
is  the  only  shape  of  shadow  a  sphere  can  give  ?    Why  ?    What  sug- 
gestions, in  these  answers,  of  a  way  to  prove  the  shape  of  the  earth  ? 

6.  Occasionally  a  "  new  star  "  is  seen  in  the  heavens.  Did  the 
phenomena  that  make  it  visible  take  place  recently  or  long  ago  ? 

Problems 

1.  A  box  1  ft.  square  has  a  small  hole  in  the  middle  of  one  side 
and  a  ground-glass  plate  for  the  opposite  side.     What  is  the  length 
of  the  image  formed  on  the  ground  glass,  of  a  window  5  ft.  high, 
at  a  distance  of  12  ft.  from  the  hole  in  the  box  ? 

2.  A  pinhole  image  of  a  house  is  5  in.  high,  the  screen  is  8  in. 
from  the  pinhole,  and  the  house  is  100  ft.  from  the  camera.     How 
high  is  the  house  ? 

3.  The  moon  is  238,840  mi.  from  the  earth.     How  long  after 
its  edge  comes  between  the  earth  and  the  sun  does  the  eclipse  begin 
to  be  seen  ? 

4.  If  the  sun  were  suddenly  extinguished,  how  long  before  its 
light  would  cease  to  reach  the  earth? 

6.  If  the  distance  from  the  earth  to  Jupiter  is  390,000,000  mi., 
how  long  after  one  of  Jupiter's  moons  passes  into  the  shadow  of  the 
planet  is  the  eclipse  observed  on  the  earth  ? 

6.  Alpha  Centauri,  the  nearest  of  the  fixed  stars,  is  not  less  than 
20,000,000,000,000  miles  from  the  solar  system.     About  how  many 
days  does  it  take  for  the  light  to  come  from  the  star  to  the 
earth? 

7.  If  a  16-candle-power  lamp  is   1.3  m.  from  a  Bunsen  pho- 
tometer screen,  how  far  must  a  20-candle-power  lamp  be  on  the 
other  side  when  the  spot  box  is  properly  adjusted? 


THE  REFLECTION  OF  LIGHT  443 

8.  How  far  must  an  800-candle-power  arc  lamp  be  from  the  same 
screen  for  equal  illumination  ? 

9.  What  is  the  candle  power  of  a  lamp  that  gives  the  same 
illumination  at  a  distance  of  5.2  m.  ? 

10.  The  two  sides  of  a  Joly  screen  appear  equally  bright  when 
placed  3  ft.  from  a  kerosene  lamp  and  5  ft.  from  an  incandescent 
lamp.  How  do  the  lamps  compare  in  the  amount  of  light  given  out  ? 

II.     THE   REFLECTION   OF   LIGHT 

488.  Reflected    and    Diffused    Light.  —  Whenever   light 
strikes  upon  a  highly  polished  surface,  the  greater  part  of 
the  light  will  be  reflected  regularly,  a  parallel  beam  being 
reflected  as  a  parallel  beam.     If,  however,  the  surface  is  not 
polished,  the  reflected  rays  are  not  parallel  but  are  scat- 
tered, and  diffused  light  is  the  result.     Bodies  that  are  not 
self-luminous  are  made  visible  by  the  light  which  they  dif- 
fuse.    A  perfectly  reflecting  surface  is  invisible. 

Demonstration.  —  Let  a  beam  of  sunlight  strike  upon  a  mirror 
and  it  will  be  reflected,  giving  a  brilliant  spot  of 
light  upon  the  wall.      Replace  the  mirror  by  a 
sheet  of  plain  white  paper  and  the  light  will  be 
scattered  or  diffused.      Each  ray  of  light  is  re- 
flected according  to  the  law  of  reflection,  but  the  -pIO 
unevenness  of  the  surface  of  the  paper  causes  the 
reflected  rays  to  scatter  in  various  directions,  as  shown  in  Fig.  453. 

489.  Reflection.  —  Demonstration.  — Through  a  small  hole  in 
the  shutter  of  a  darkened  room  admit  a  ray  of  sunlight.     Lay  a 
mirror  in  its  path  and  scatter  crayon  dust  or  smoke  in  the  air.     A 
large  part  of  the  light  is  reflected.     Observe  that  the  reflected  ray- 
is  straight  and  that  its  direction  depends  upon  the  angle  at  which  the 
ray  strikes  the  mirror. 

In  Fig.  454,  if  L  is  the  source  of  light,  MM'  the  reflecting 
surface,  P  the  point  at  which  a  ray  of  light  strikes  it,  and 


444 


LIGHT 


PH  the  normal  or  perpendicular  to  the  reflecting  surface 
at  the  point  P,  then  LP  is  called  the  incident  ray,  PB  the 

reflected  ray,  the  angle  LPH 
the  angle  of  incidence,  which 
is  the  angle  between  the 
perpendicular  HP  and  the 
-M'  incident  ray,  and  BPH  the 
angle  of  reflection. 


P 

FIG.  454 


490.  The  Laws  of  Reflection. 

I.  The  angle  of  reflection  is  equal  to  the  angle  of  incidence 
and  is  in  the  same  plane. 

II.  The  plane  including  the  incident  and  reflected  rays  is 
perpendicular  to  the  reflecting  surface. 

491.  The  Hart!  Optical  Disk  is  so  well  adapted  to  the  dem- 
onstration of  the  fundamental  phenomena  of  light,  that  its 
use  is  recommended  for  class  demonstrations.     A  dark  room 
is  not  necessary,  as  the  disk  will  show  the  phenomena  in  an 
ordinary  room.     Sunlight  is  the  best  source  of  light  to  use 
with  it,  out  an  arc  lamp,  an  incandescent 

lamp,  or  a  mantle  lamp  will  do. 

Demonstration.  —  Figure  455  shows  the  ap- 
paratus in  use  to  demonstrate  the  laws  of  re- 
flection from  a  plane  mirror.  The  graduated 
scale  and  the  semicircular  sheet-metal  screen 
are  capable  of  rotating  independently  on  the 
same  axis.  On  sending  a  beam  of  sunlight 
through  the  opening  in  the  screen,  letting  the 
smaller  beams  strike  upon  a  mirror  fixed  to  the 
disk,  and  turning  the  disk  until  the  beams  strike  at  an  angle  to  the 
zero  line,  it  will  tfe  seen  that  the  reflected  beams  make  the  same 
angle  with  the  zero  line,  or  normal,  that  the  incident  beams  make 
with  the  same  line. 


FIG.  455 


THE   REFLECTION   OF  LIGHT  445 

492.  Plane  Mirrors  and  their  Images.  —  A  plane  mirror 
is  a  plane  surface  that  reflects  regularly  a  large  part  of  the 
light  that  falls  upon  it.     If  a  person  stands  in  front  of  a 
plane  mirror,  he  sees  his  image  apparently  behind  it.     If 
he  walks  toward  the  mirror,  the  image  does  the  same.     If 
he  steps  to  one  side,  the  image  does  also.     If  he  looks  at  the 
image  of  a  stationary  object,  it  remains  in  the  same  place 
however  much  he  changes  his  position.     This  kind  of  image 
is  called  a  virtual  image  because  it  does  not  really  exist  at 
the  place  where  it  appears  to  be,  but  is  caused  by  divergent 
rays  of  light  that  come  from  the  object  and  are  reflected  from 
the  mirror. 

493.  To  locate  the  Image  of  a  Point.  —  Let  A  (Fig.  456) 
be  the  point,  the  image  of  which  is  to  be  found.     Since  the 
angle  of  reflection  is  equal  to 

the  angle  of  incidence,  the  ray 
AB,  perpendicular  to  the  sur- 
face, will  be  reflected  upon  it- 
self in  the  direction  BA ;  and 
the  image  of  the  point  A  will 
be  on  BA  or  AJ3  prolonged. 
Any  other  ray  AC  will  be  re- 
flected as  CE,  making  the  angle  of  reflection  1$CD  equal  to 
the  angle  of  incidence  A£D ;  and  the  image  will  be  on  CE 
or  EC  nrolonged.  As  the  lines  BA  and  CE  are  divergent 
in  front  of  the  mirror,  their  only  point  of  intersection  is  at  A', 
a  point  behind  the  mirror,  which  is  the  image  of  A. 

From  the  figure  the  triangles  ABQ  and  ALEC  are  right 
triangles,  and  the  line  BQ  is  common.  The  angles  ACB  and 
ECM'  are  equal,  since  ECU  =  ACD.  ^But_^OIB  also  equals 
ECM' ;  hence  the  angle  ACB  equals  the  angle  A'CB,  and  the 


446 


LIGHT 


FIG.  457 


triangles  ABC  and  A' EC  are  equal  in  all  their  parts.  Hence 
A'E  =  AB.  This  means  that  the  image  of  a  point  in  a  plane 
mirror  is  on  a  perpendicular  from  the  point  to  the  mirror  and 
as  far  behind  the  mirror  as  the  object  is  in  front  of  it. 

494.  To  locate  the  Image  of  an  Object.  —  If  the  object  is 
a  straight  rod  like  the  arrow  AB  in  Fig.  457^  it  will  be  neces- 

sary  to  determine  the  posi- 
tion of  the  image  of  each  end, 
only  as  all  intermediate  points 
will  be  found  on  the  straight 
B  line  which  joins  them.  The 


points  A'  and  B'  are  found 
by  §  493.  The  paths  taken 
by  the  rays  that  enter  the 
eye  at  E  may  be  shown  by 
finding  the  points  C  and  D,  where  straight  lines  from  the 
points  A'  and  B'  to  the  eye  intersect  the  mirror.  The 
incident  rays,  then,  will  be  AC  and  BD,  and  the  reflected 
rays  will  be  CE  and  DE.  When  the  eye  is  at  E,  the  only 
part  of  the  mirror  used  is  CD.  An  eye  placed  at  E'  would 
see  the  image  likewise  at  A'B',  but  would  use  an  entirely 
different  part  of  the  mirror. 

Demonstrations.  —  Place  a  mirror  horizontally  on  a  table  and 
look  at  the  image  of  a  candle  placed  the  other  side  of  the  mirror  from 
the  eye.  What  kind  of  inversion  is  caused  by  a  horizontal cairror? 

Stand  at  a  distance  in  front  of  a  small  plane  mirror  placed  verti- 
cally against  the  wall.  Notice  how  much  of  your  figure  you  can  see ; 
then  walk  toward  the  mirror,  and  observe  whether  any  greater 
length  of  the  figure  can  be  seen.  Explain. 

Stand  in  front  of  a  plane  mirror  With  the  right  hand  raised. 
Which  hand  of  the  image  is  raised?  What  kind  of  inversion  is 
caused  by  a  vertical  mirror? 


THE   REFLECTION  OF  LIGHT 


447 


FIG.  458 


495.  Multiple  Images  from  Mirrors  at  an  Angle.  —  If  two 
mirrors  are  placed  at  a  right  angle  with  each  other,  as  M 
and  M'  (Fig.  458),  the 

object  being  at  A  and 

the  eye  at  E,  then  there 

will  be  seen  an  image 

A'  in  the  mirror  M,  a 

second  image  A"  in  the 

mirror  M' ,  and  a  third 

A'",  which  is  the  image 

in  M'  of  the  image  A' 

formed   by   the   mirror 

M.      The   positions  of 

all  these  images  may  be 

found  by  applying  the 

rule  for  finding  the  image  of  a  point  in  a  plane  mirror  (§  493). 

The  paths  of  the  rays  that  enter  the  eye  may  be  found  as 

is  shown  in  the  figure. 

Multiple  images  formed  in  two  mirrors  that  are  inclined 

at  a  less  angle  than  90°  can 
be  studied  by  a  pair  of  hinged 
mirrors,  such  as  are  shown  in 
Fig.  459.  By  standing  the 
mirrors  on  a  table  and  vary- 
ing the  angle  between  them, 
the  relation  between  the  angle 
and  the  number  of  images  can 
FIG.  459  be  shown. 

496.  Multiple  Images  from  Parallel  Mirrors.  —  If  two  mir- 
rors MM'  and  NNf  are  placed  parallel  and  facing  each  other, 
several  images  of  the  candle  C  will  be  seen  by  the  eye  E, 


448 


LIGHT 


placed  as  in  Fig.  460.     What  may  be  called  primary  images, 
formed  by  one  reflection,  will  be  seen  in  the  directions  EA 


cr 

\M 


..  B 


N' 


FIG.  460 

and  EA'.  Secondary  images,  formed  by  two  reflections, 
will  be  seen  in  the  directions  EB  and  EB'.  The  images  of 
the  candle  appear  at  C'  and  C". 

Demonstrations.  —  Place  four  long,  narrow  strips  of  mirror 
inside  a  long  narrow  box,  fastening  them  to  the  four  sides.  Make  a 
cover  for  one  end  and  bore  a  small  hole  in  the  middle  of  it.  Place 
the  eye  at  the  opposite  end  of  the  box  and  direct  the  box  toward 
a  window.  Observe  the  different  images  seen  from  the  four  sides. 

Strips  of  window  glass  backed 
with  black  paper  will  do  very 
well  if  mirrors  cannot  be  ob- 
tained. 


497.  Multiple  Images 
formed  by  a  Plate-glass 
Mirror.  —  When  light  from 
any  source,  as  the  point 
P  (Fig.  461),  falls  upon  a 


P[  FIG.  461 


THE   REFLECTION   OF  LIGHT  449 

plate-glass  mirror,  two  images  will  be  formed :  one  at  P' 
from  the  upper  surface  MM',  and  one  at  P"  from  the  lower 
surface  NNf.  The  image  Pr  is  generally  faint,  as  but  little 
of  the  light  striking  MM'  is  reflected  from  that  surface, 
the  most  of  it  passing  through  to  the  surface  NN',  from  which, 
as  the  glass  has  a  mercury  back,  it  is  nearly  all  reflected. 
The  reason  for  the  bending  of  the  ray  at  A  and  C  will  be  ex- 
plained under  the  subject  Refraction. 

By  holding  a  lamp  close  to  a  plate-glass  mirror  and  looking  at  its 
image  in  a  slanting  direction  several  images  will  be  seen.  Two  of 
these  are  like  P'  and  P"  (Fig.  461) ;  the  others  are  due  to  rays  strik- 
ing the  mirror  at  the  left  of  A  and  emerging  at  the  right  of  C  after 
several  reflections  between  NNf  and  MM'. 

498.  Concave  Mirrors  may  be  formed  of  the  concave 
surfaces  of  either  spheres  or  paraboloids,  hence  the  sections 
of  concave  mirrors  by  a  plane  will  be  arcs  of  either  circles 
or  parabolas.  If  C  is  the  center  of  the  sphere  from  which 
the  mirror  in  Fig.  462  is  formed,  and  MN  the  section  of 
the  mirror,  then  C  is  the  center  of  curvature,  A  is  the  center 
of  the  mirror,  CA  is  the  principal  axis,  any  other  axis,  as 
EB,  is  a  secondary  axis,  and  MCN  is  the  aperture  of  the  mirror. 
In  the  treatment  which  follows  (§§  499-505),  the  aperture 
of  the  mirror  is  supposed  to  be  not 
more  than  10°  or  12°,  but  in  order 
to  construct  the  geometrical  figures 
clearly  it  is  taken  much  greater. 


499.  Foci.  —  A  focus  is  a  point  to    E' 

which  rays  of  light  converge,  or  from 

which  they  diverge.      The  principal 

'focus  of  a  mirror  is  the  point,  on  the  principal  axis,  in  which 

rays  of  light  parallel  to  that  axis  meet  after  being  reflected 

Rev. 


450  LIGHT 

from  the  mirror.  The  distance  of  this  point  from  the  mirror 
is  the  principal  focal  length.  A  focus  is  real  when  it  is  caused 
by  the  meeting  of  rays  of  light,  and  virtual  when  rays  appear 
to  come  from  it. 

500.  Foci  of  Concave  Mirrors.  —  There  are  six  cases  that 
can  be  considered. 

(a)  When  the  Source  of  Light  is  at  an  Infinite  Distance. 

—  In  this  case  the  rays 
of  light  will  be  parallel 
to  the  principal  axis.  The 
direction  of  the  reflected 

FIG.  463 

ray  MF  (Fig.  463)  is  de- 
termined by  drawing  the  normal  from  M  to  the  center 
of  curvature  C,  and  making  the  angle  of  reflection  CMF 
equal  to  the  angle  of  incidence  CMD.  This  reflected  ray 
will  cut  the  principal  axis  in  F,  a  point  practically  halfway 
between  C  and  A.  By  a  similar  construction  it  can  be  shown 
that  other  parallel  rays  will  pass  through  F;  hence  F  is  at 
the  principal  focus. 

(b)  When  the  Source  of  Light  is  at  a  Finite  Distance  be- 
yond the  Center  of  Curvature.  —  In  this  case  the  rays  of  light 
will  diverge,  as  from  the  point  P  (Fig. 

464).  The  direction  of  any  ray,  as 
PM,  after  reflection  is  found  by  mak- 
ing the  angle  CMP'  equal  to  the  angle 
CMP.  Other  rays  from  P  striking  the 
mirror  will,  after  reflection,  meet  at  P', 
which  is  a  point  between  the  center  of  curvature  and  the 
principal  focus. 

(c)  When  the  Source  of  Light  is  at  the  Center  of  Curvature. 
—  Since  every  line  from  the  center  of  curvature  to  the 


THE   REFLECTION   OF  LIGHT 


451 


CS  F 


mirror  is  a  radius  of  the  mirror,  it  is  evident  that  the  focus 
will  be  found  at  C. 

(d)  When  the  Source  of  Light  is  between  the  Center  of  Cur- 
vature and  the  Principal  Focus.  —  This  is  the  converse  of 
case'  (6),  and  by  reference  to  Fig.  464  it  will  be  seen  that 
the  focus  of  P'  is  P,  a  point  beyond  the  center  of  cur- 
vature. 

(e)  When  the  Source  of  Light  is  at  the  Principal  Focus. 
—  This  is  the  converse  of  case  (a).     When  the  source  of 
light  is  at  F  (Fig.  463),  the  direction  of  every  ray  after 
reflection  will  be  parallel  to  the  principal  axis ;    that  is,  the 
focus  will  be  at  an  infinite  dis- 
tance —  in  other  words,   there 

will  be  no  focus. 

(f)  When  the  Source  of  Light 
is  between  the  Principal  Focus 
and  the  Mirror.  —  By  making 
the    angle    of    reflection    equal 

to  the  angle  of  incidence  CMP  (Fig.  465),  it  will  be  seen 
that  the  reflected  rays  diverge  from  the  principal  axis  as 
though  they  came  from  a  point  P'  behind 
the  mirror.  This  point  P'  is  a  virtual 
focus. 

Demonstration.  —  By  allowing  parallel  rays 
of  light  to  fall  upon  the  screen  of  the  optical 
disk,  the  location  of  the  principal  focus  of  a 
concave  mirror  can  be  readily  seen.  The 
principal  focal  length  is  practically  half  the 
FIG.  466  radius  of  the  mirror. 

501.  Focus  of  a  Point  not  in  the  Principal  Axis.  —  If  the 
source  of  light  is  not  in  the  principal  axis,  its  focus  may  be 
found  by  the  following  simple  construction.  Draw  from  the 


FIG.  465 


452 


LIGHT 


point  P  (Fig.  467)  a  secondary  axis  through  C.  The  ray  sent 
in  this  direction  will  be  reflected  on  itself.  Draw  a  ray  paral- 
lel to  the  principal  axis,  as  PM.  It 
will  be  reflected  through  F,  and  its 
intersection  with  NC  will  determine 
the  point  P',  the  focus  of  rays  com- 
FIQ.  467  ing  from  P. 

502.  Conjugate  Foci.  —  By  a  study  of  the  relation  between 
the  position  of  the  point  of  light  and  its  focus  it  is  seen  that 
in  all  cases  in  which  there  is  a  real  focus,  the  point  of  light 
and  its  focus,  or  image,  are  interchangeable.     If  a  candle 
is  used  at  P,  its  image  is  found  at  P1 '.     If  now  the  candle  is 
placed  at  P',  its  image  is  at  P.     Two  points,  so  located  that 
one  is  the  image  of  the  other,  arev  conjugate  foci. 

503.  Images  formed    by  Concave  Mirrors.  —  The  geo- 
metrical construction  of  images  formed  by  concave  mir- 
rors is  practically  the  determination  of  the  foci  of  points. 
To  make  this  construction  but  two  rays  are  necessary  for 
each  point,  since  the  intersection  of  any  two  reflected  rays 
determines  the  image  of  a  point.     By  using  the  ray  passing 
through  C,  which  is  a  secondary  axis,  and  the  ray  parallel 
to  the  principal  axis,  only  three 

lines  need  be  drawn. 

(a)  When  the  Object  is  at  an  In- 
finite Distance.  —  Since  the  focus 
of  rays  parallel  to  the  principal 
axis  is  at  the  principal  focus,  the 
image  will  be  at  F,  and  will  be 

a  point.  FIG-468 

(b)  When  the  Object  is  at  a  Finite  Distance  beyond  the 
Center  of  Curvature.  —  Following  the  rule  for  construction 


THE  REFLECTION  OF  LIGHT 


453 


FIG.  469 


given  above,  the  points  A'  and  E'  (Fig.  468)  are  found. 
These  being  the  extreme  points  of  the  image,  all  other  points 
lie  between  them.  The  image  is  real,  in- 
verted, smaller  than  the  object,  and  be- 
tween the  center  of  curvature  and  the  focus. 

(c)  When  the  Object  is  at  the  Center  of 
Curvature.  —  In  this  case,  Fig.  469  shows 
that  the  image  will  be  real,  inverted,  of 
the  same  size  as  the  object,  and  at  the 
center  of  curvature. 

(d)  When  the  Object  is  between  the  Center  of  Curvature  and 
the  Principal  Focus.  —  This  is  the  reverse  of  case  (6),  and 

Fig.  470  shows  that  the  image  is 
real,  inverted,  larger  than  the  ob- 
ject, and  beyond  the  center  of 
curvature. 

(e)  When  the  Object  is  at  the 
Principal  Focus.  —  This  is  the  re- 
verse of  case  (a).  The  rays  are 
sent  off  in  parallel  lines  ;  hence  the 

image  is  at  an  infinite  distance  away ;  that  is,  there  is  none. 
(/)   When  the  Object  is  between  the  Principal  Focus  and 

the   Mirror.  —  In    this 

case,   as    shown    in   Fig. 

471,    the    reflected    rays 

are  divergent,  and  there 

can    be    no    real    image. 

By  prolonging  these 

rays  behind  the  mirror, 

however,    the    image    is 

seen    to    be   virtual,    upright,    and    larger    than    the   ob- 
ject. 

Rev. 


FIG.  470 


FIG.  471 


454 


LIGHT 


504.  Relative  Size  of  Object  and  Image.  —  To  get  an 

expression  for  the  relation  between  the  size  of  the  object 
and  that  of  its  image,  it  is  only  necessary  to  study  the  geo- 
metrical construction  of  such  a  figure  as  that  in  case  (6). 
From  similar  triangles  in  Fig.  468  it  is  seen  that  AB :  A'E' 
=  CD :  CD'.  That  is,  the  length  of  the  object  is  to  the  length 
of  the  image  as  the  distance  of  the  object  from  C  is  to  the  dis- 
tance of  the  image  from  C.  Experiment  shows  that 


1  =  1+1, 

F      D 


(62) 


in  which  F  is  the  principal  focal  length,  or  practically  half 
the  radius  of  curvature,  D0  the  distance  of  the  object  from 
the  mirror,  and  DI:  the  distance  of  its  image.  From  this 
formula  any  one  of  these  three  distances  can  be  found 
if  the  other  two  are  known. 

505.  The  Convex  Mirror.  —  If  the  outside  of  a  sphere  is 
made  the  reflecting  surface,  the  mirror  is  convex.     The  focus 

and  image  are  de- 
termined as  in  the 
case  of  the  concave 
mirror,  except  that 
the  reflected   rays 
7  must  be  prolonged 
behind  the  mirror 
before  they  meet, 
,  and  hence  the  im- 

FIG.  472     ' 

age  is  a  virtual  one. 

It  is  also  upright  and  smaller  than  the  object,  as  a  construc- 
tion like  Fig.  472  will  show. 

Demonstrations.  —  Using  two  mirrors,  one  concave  and  the  other 
convex,  verify  the  statements  in  §§  503-505.     Observe  that  the  real 


THE   REFLECTION   OF  LIGHT  455 

image  can  be  caught  on  a  screen,  while  the  virtual  cannot,  though 
both  alike  can  be  seen  with  the  mirror.  A  piece  of  ground  glass 
forms  an  excellent  screen. 

Hang  a  concave  mirror  on  the  wall  so  that  its  center  is  at  the 
height  of  the  eye.  Let  two  students  of  the  same  height  stand  in 
front  of  the  mirror  10  or  15  feet  away.  While  one  watches  the 
image  of  the  second,  let  the  second  walk  slowly  toward  the  mirror. 
By  careful  observation,  student  No.  1  can  see  the  inverted  image 
of  the  face  of  student  No.  2  advance  from 
the  mirror  and  finally  rest  upon  the  shoul- 
der of  No.  2  when  he  is  at  the  center  of  cur- 
vature. 

If  the  concave  mirror  used  in  Fig.  466  is 
turned  over,  its  opposite  side  can  be  used  for 
a  convex  mirror.  Figure  473  shows  how  a 
group  of  parallel  rays  are  reflected  as  a  di- 
verging pencil.  The  focus  of  these  rays  can  be 
found  by  projecting  the  outer  rays  behind  the  *~  FIG.  473 
mirror.  From  this  position  the  focal  length 
can  be  found ;  it  will  be  practically  half  the  radius  of  curvature. 

506.  Spherical  Aberration.  —  If  the  angular  opening  of 
the  concave  mirror  is  large,  the  principal  focus  for  parallel 
rays  near  the  axis  will  be  farther  from  the  mirror  than  that 
for  those  near  its  edge  (Fig.  474).  For  this  reason  the  out- 
side of  an  image  some- 
time looks  blurred.  To 
prevent  this  spherical  aber- 
ration the  aperture  should 
0  '  not  exceed  10°  or  12°. 

Spherical    aberration    can 

be  avoided  by  the  use  of  parabolic  mirrors,  such  as  are  used 
in  headlights  for  locomotives  and  electric  cars.  The  rays  of 
light  coming  from  a  lamp  in  the  focus  of  such  a  mirror  are 
sent  off  as  parallel  rays. 


456  LIGHT 

Questions 

1.  Define  the  angle  of  reflection. 

2.  Refer  to  Fig.  460  and  show  how  you  determine  the  positions 
of  C'  and  C" '. 

3.  What  relation  is  there  between  the  first  and  second  of  the  mul- 
tiple images  in  a  plate-glass  mirror  and  the  thickness  of  the  glass  ? 

4.  What  difference  is  there  between  the  image  that  a  person  sees  of 
himself  in  a  mirror  and  the  appearance  he  presents  to  other  people  ? 

5.  Prove  that  the  shortest  plane  mirror  in  which  you  can  see 
your  entire  figure  when  you  are  standing  erect  and  the  mirror  is 
vertical,  is  one  half  your  height. 

6.  Where  must  the  light  be  placed  if  the  concave  mirror  of  an 
automobile  lamp  is  to  throw  a  parallel  beam  of  light? 

7.  What  effect  will  it  have  upon  the  shape  of  the  beam  to  bring 
the  lamp  nearer  the  mirror? 

8.  Describe  the  changes  that  take  place  in  the  image  of  an  object 
when  it  is  brought  from  an  infinite  distance  to  the  surface  of  a  con- 
cave mirror.     Consider  location,  position,  size,  and  character  of  the 
image. 

9.  What  are  the  distinguishing  characteristics  of  the  image  seen 
in  a  convex  mirror  ? 

Problems 

1.  What  is  the  angle  of  incidence  when  the  angle  between  the 
incident  and  reflected  rays  is  38°  ? 

2.  The  sun  is  40°  above  the  horizon.     What  is  the  angle  of  inci- 
dence when  its  light  shines  upon  the  surface  of  a  pond  ? 

3.  A  boy  stands  6  feet  in  front  of  a  vertical  plane  mirror.     What 
is  his  distance  from  his  image  ? 

4.  The  point  of  a  pencil  is  placed  on  the  front  surface  of  a  piece 
of  plate  glass  and  the  image  is  one  inch  from  the  point.     How  thick 
is  the  glass  ? 

5.  A  lamp  is  placed  one  foot  in  front  of  a  vertical  plate  of  glass 
three  quarters  of  an  inch  thick.     What  is  the  distance  between  the 
two  images? 

6.  A  concave  mirror  has  a   radius  of  curvature   of  4  ft.     At 
what  distance  from  the  mirror  is  the  image  of  the  sun  formed  by  it  ? 


REFRACTION   OF  LIGHT 


457 


FIG.  475 


7.  A  rod  18  in.  long  is  placed  erect  6  ft.  in  front  of  this  mirror. 
How  far  in  front  of  the  mirror  will  its  image  be  ?     What  will  be  its 
length?     Solve  by  construction.     Solve  also  by  Formula  62. 

8.  A  man  standing  8  ft.  in  front  of  two  mirrors,  one  concave  and 
the  other  convex,  observes  his  image  in  each.     What  is  the  differ- 
ence between  them  if  each  has  a  radius  of  4  ft.  ? 

III.    REFRACTION   OF  LIGHT 

507.  Refraction.  —  If  a  heavy  pencil  line  is  drawn  on 

a  sheet  of  paper  and  a  piece  of  plate  glass  is  laid  over  it, 

the   line   seen   through   the   glass 

will  be  a  continuation  of  the  part 

that  the  glass  does  not  cover,  as 

in  (a),  Fig.  475,  provided  the  eye 

is  directly  in  front   of   the   line. 

If,  however,  it  is  on  one  side,  the 

line  will  appear  to  be  a  broken  line  as  in  either  (6)  or  (c). 

The  reason  for  this  appearance  is  that  the  light  coming  from 

the  line  to  the  eye  has  its 
direction  changed  at  the 
surface  of  the  glass.  This 
bending  of  the  ray,  called 
refraction,  takes  place 
whenever  light  passes 
obliquely  from  one  me- 
dium into  another  of  dif- 
ferent optical  density. 

508.   Angles    of    Inci- 
dence and  Refraction.  - 
Water  is  optically  denser 
than  air.     Let  the  incident  ray  AB  (Fig.  476)  strike  the 
surface  of  water  at  B.    Part  of  the  light  will  be  reflected, 


FIG.  476 


458 


LIGHT 


part  absorbed,  and  part  will  pass  through  the  water. 
This  last  part,  the  refracted  ray,  will  take  the  direction 
BC.  Draw  the  normal  DE  to  the  surface  at  B ;  then  the 
angle  ABD  is  called  the  angle  of  incidence,  and  the  angle 
EBK  the  angle  of  refraction.  The  angle  CB L,  which  is  the 
difference  between  the  angles  of  incidence  and  refraction, 
is  the  angle  of  deviation. 

509.  Cause  of  Refraction.  —  When  a  beam  of  light  mov- 
ing in  one  medium  strikes  the  surface  of  another,  the  part 
that  enters  the  new  medium  will  have  its  velocity  changed. 
If  the  new  medium  is  optically  denser  than  the  old,  the 
velocity  will  decrease,  while  if  it  is  optically  rarer,  the  velocity 
will  increase. 

Suppose  the  beam  has  the  wave  front  LF  (Fig.  477)  and 
is  moving  in  the  direction  CD.  When  the  ray  EF  passes 
the  surface  xy,  its  velocity  in  the  new  medium  is  less,  and  by 
the  time  the  ray  AL  has  reached  B,  the  ray  EF  will  have 
gone  only  the  distance  FG  from  F,  the  ray  CD  will  have 
reached  H,  the  new  wave  front  will  be  EG,  and  as  the  direc- 
4  tion  of  light  is  always  per- 

pendicular to  the  wave 
front,  the  new  direction 
will  be  DH. 


510.  Index  of  Refrac- 
tion. —  If  Fig.  477  repre- 
sents light  passing  from 
air  into  water,  FG  is  the 
distance  the  light  travels 
in  water  while  it  travels  the  distance  LB  in  air.  Hence 
LB  :  FG  =  V  :  v,  where  V  and  v  are  the  velocities  in  air 


FIG.  477 


REFRACTION  OF  LIGHT  459 

and  water  respectively.      Since  V  and  v  are  constant  veloc- 
ities the  ratio  —  must  also  be  a  constant  and  this  is  called 
v 

the  index  of  refraction. 

The  index  of  refraction  is  a  constant  for  all  angles  of  inci- 
dence and  is  the  same  as  the  ratio  of  the  velocities  of  light  in  the 
two  media. 

511.  The  Laws  of  Refraction. 

I.  When  a  ray  of  light  passes  obliquely  from  an  optically 
rarer  to  an  optically  denser  medium,  it  is  bent  toward  the  per- 
pendicular to  the  surface  at  that  point.     When  it  passes  from 
an  optically  denser  to  an  optically  rarer  medium,  it  is  bent  from 
the  perpendicular. 

II.  The  incident  and  refracted  rays,  and  the  normal  to  the 
refracting  surface,  are  in  the  same  plane. 

III.  Whatever  the  incident  angle,   the  index  of  refraction 
for  any  two  media  is  a  constant  quantity. 

512.  Indices  of  Refraction.  —  Since  the  ether  is  the  real 
medium  for  the  transmission  of  light,  and  since  the  velocity 
is  greater  in  ether  alone  (i.e.,  in  a  vacuum)  than  in  ether 
associated  with  any  kind  of  matter,  there  are  two  kinds 
of  indices  of  refraction :  one  is  the  absolute  index,   shown 
when  the  ray  passes  from  a  vacuum  into  a  substance;  the 
other  is  the  relative  index,  shown  when  the  ray  passes  from 
one  substance  into  another. 

The  relative  index  of  two  substances  is  found  by  taking 
the  inverse  ratio  of  their  absolute  indices.  Approximately, 
the  index  of  refraction  for  light  passing  from  air  to  water 
is  taken  as  f ;  to  crown  glass,  f ;  to  flint  glass,  -f ;  and  to 
diamond,  |. 


460 


LIGHT 


TABLE  OF  ABSOLUTE  INDICES  OF  REFRACTION  (YELLOW  LIGHT) 
Vacuum 1.00000    Carbon  Bisulphide     .     .     1.624 


Air 1.00029 

Water 1.334 

Alcohol .  1.360 


Crown  Glass     ....     1.516 

Flint  Glass 1.651 

Diamond  .    2.47  to  2.75 


513.  Total  Reflection;  Critical  Angle.  —  Demonstration.  - 

Fix  on  the  optical  disk  a  semicircular  piece  of  plate  glass,  as  in 
Fig.  478.  Rotate  the  shield  and  allow  a  single 
narrow  band  of  light  to  strike  on  the  cylindri- 
cal surface  at  various  angles  to  the  horizontal. 
At  some  angles  the  beam  on  reaching  the  plane 
side  of  the  glass  will  be  reflected  back  into  the 
glass  and  pass  out  at  the  upper  surface.  At 
other  angles  part  of  the  beam  will  pass  through 
the  glass,  undergoing  refraction  as  it  leaves 
the  plane  surface.  At  a  certain  angle  of  inci- 
dence the  refracted  beam  will  just  graze  the 
FIG.  478  plane  surface  of  the  glass. 

This  angle  of  incidence,  where  total  reflection  begins, 
is  called  the  critical  angle,  and  varies  with  the  media.  The 
critical  angle  for  light  passing  from  water  into  air  is  about 
48.5°;  from  crown 
glass  into  air,  42°; 
and  from  diamond 
into  air,  24°. 


514.  Effect  of 
Total  Reflection.— 
If  a  luminous  point 
is  placed  at  the  bot- 
tom of  a  vessel  of 
water  (Fig.  479),  it 
will  send  rays  of  light  in  all  directions.  All  the  rays  that  are 
within  a  cone,  having  its  apex  at  the  luminous  point  and 


REFRACTION  OF  LIGHT 


461 


its  base  in  the  surface  of  the  water,  including  an  angle  of  97°, 
will  pass  out  into  the  air.  All  rays  outside  of  this  cone  will 
be  reflected  from  the  surface  back  into  the  water.  This 
means  that  the  entire  space  above  the  water  would  be  seen 
by  'an  eye  looking  upward  from  beneath  the  surface,  within  a 
circle  limited  by  a  cone  of  rays, 
the  angle  between  any  two  rays 
on  opposite  sides  of  the  cone 
being  97°.  Beyond  that  circle, 
the  surface  of  the  water  acting 
as  a  total  reflector  would  reflect 
the  bottom  and  things  lying 
upon  it. 

515.     Total  Reflecting  Prism.  Fig.  480 

-Let  ABC,  (Fig.  480), represent 

a  right-angled  prism  the  cross  section  of  which  is  an  isosceles 

triangle.  A  ray  of  light  from 
P,  "perpendicular  to  AB,  will 
pass  through  it  without  change 
of  direction,  will  strike  the  face 
BC  at  an  angle  of  45°  and,  since 
this  is  greater  than  the  critical 
angle,  will  be  totally  reflected 
and  pass  out  normal  to  the  sur- 
face AC.  A  prism  of  this  shape, 
with  polished  faces,  is  one  of  the 
most  perfect  reflectors  known. 
For  this  reason  it  is  used  in 
many  optical  instruments. 

The  direction  of  any  partic- 
FIG.  481  ular  ray  can  be  traced  from  the 


462 


LIGHT 


water  to  the  air  as  in  Fig.  481 .  Let  PB  be  the  ray,  the  path 
of  which  is  to  be  determined.  With  B  as  a  center  and  BP  as 
radius,  describe  an  arc  to  the  right  of  the  normal  BC.  Meas- 
ure NB  and  lay  off  four  thirds  of  this  distance  as  CD  so  that 

D  shall  be  on  the  arc. 
Then  BD  will  be  the 
^  direction  taken  by  the 

\  ray  PB. 

A  To    determine    the 

critical  angle,  take  the 
ray  LP  passing  along 
the  surface  of  the 
water  (Fig.  482),  and 
let  it  be  required  to 
find  the  direction  it  will  take  in  the  water.  With  P  as  a 
center  and  any  distance  PA  as  radius,  describe  an  arc  above 
LP.  Lay  off  PB  equal  to  three  fourths  of  PA  and  from  B 
erect  a  perpendicular  BD.  From  P  draw  the  line  PC  as  a 
continuation  of  the  direction  DP  and  the  angle  CPN  is  the 
critical  angle.1 

Demonstrations.  —  Hold  a  glass  of  water  high,  and  look  through 
the  side  of  the  glass  at  the  surface  of  the  water.  Notice  that  you 
cannot  look  through  the  surface.  Put  a  spoon  into  the  glass,  and 
notice  that  the  part  in  the  water  is  reflected  from  the  surface. 

Fill  a  beaker  two  thirds  full  of  water.  Into  this  thrust  a  test  tube 
with  a  long,  narrow  slip  of  paper  in  it.  Notice  that  there  is  a  posi- 
tion at  which  total  reflection  takes  place  and  the  paper  cannot  be 
seen  through  the  water.  Pour  a  little  water  into  the  test  tube,  and 
notice  that  the  paper  can  be  seen  wherever  the  tube  has  water  in  it. 

516.  Effects  of  Refraction.  Whenever  a  straight  stick 
is  placed  in  water  at  an  angle,  as  AB  (Fig.  483),  it  appears 


1  See  Appendix,  for  proof. 


REFRACTION  OF  LIGHT 


463 


FIG.  483 


bent  at  the  surface  of  the  water  D,  the  part  ED  below  the 
surface  seeming  to  rise,  the  end  B  taking  the  position  C. 
This  effect  is  due  to 
the  refraction  of  the 
ray  •  BF  at  F,  where 
it  takes  the  direction 
FE,  and  to  the  fact 
that  the  apparent  po- 
sition of  a  body  is  in 
the  direction  of  the  ray 
that  enters  the  eye. 

For  the  same  reason  a  pond  into  which  one  looks  seems 
to  be  shallower  than  it  really  is. 

Refraction  takes  place  in  gases  also,  when  rays  pass  from 
one  medium  into  another  of  different  density.  This  gives 
rise  to  two  effects  at  sunrise  and  sunset. 

First.  —  The  sun  is  seen  when  it  is  really  below  the  horizon. 
If  the  line  AB  (Fig.  484)  represents  the  horizon  at  the  point 

A,  the  sun,  though  be- 

iS 

low  it,  at  the  point  S,  ap- 
pears to  be  at  the  point 
S' :  for  the  rays  from 
S,  on  striking  the  atmos- 
phere of  the  earth  and 
constantly  passing  into  denser  layers,  are  bent  downward, 
and  as  the  ray  that  enters  the  eye  is  from  the  direction 
S'A,  this  makes  the  sun  appear  to  be  at  S'. 

Second.  — Another  effect  is  that  upon  the  apparent  shape  of 
the  sun.  The  rays  that  are  nearest  the  horizon  are  bent  the 
most,  so  that  the  lower  side  appears  higher  than  it  really  is, 
with  reference  to  the  upper  side.  This  causes  an  apparent  flat- 
tening of  the  sun  near  the  horizon,  especially  on  the  lower  side. 


FIG.  484 


464 


LIGHT 


FIG.  485 


517.  Refraction  through  Plates  with  Parallel  Sides.  — 
When  light  passes  through  the  side  of  a  transparent  plate 

with  parallel  sides,  as  at 
E  (Fig.  485),  it  is  bent 
toward  the  normal  at  E, 
taking  the  direction  EH, 
as  determined  by  the  rel- 
ative index  of  refraction, 

-.  When  the  light 
v 

reaches  H,  the  part  pass- 
ing through  is  bent  away 
from  the  normal  in  the 
direction  HK,  as  determined  by  the  relative  index  of  re- 
fraction, which  is  the  reciprocal  of  the 
first  index.  Hence  the  direction  of  H  K, 
the  emerging  ray,  is  parallel  to  LE. 

Demonstration.  — •  This  can  be  shown  by 
using  a  plate  glass  with  parallel  sides  in  the 
optical  disk.  Whatever  the  angle  of  the  inci- 
dent beam,  it  will  be  seen  that  the  emergent 

beam  is  parallel  to  it. 

OF 

518.  Prisms.  —  If  the  surfaces  of  the  FlG- 486 
transparent  medium  are  not  parallel,  the  emerging  ray  will 

not  be  parallel  to  the  inci- 
dent ray.  When  the  cross 
section  of  the  medium  is 
a  triangle,  the  medium  is 
a  prism.  The  path  of 
a  ray  passing  through  a 
prism  is  shown  in  Fig. 
FIG.  487  487.  When  the  ray  from 


REFRACTION   OF  LIGHT  465 

L  strikes  the  prism  at  D,  it  is  bent  toward  the  normal  and 
passes  through  the  prism  in  the  direction  DH.  When  it 
passes  out  of  the  prism  at  //  it  is  bent  from  the  normal  in 
the  direction  II K.  A  ray  of  light  passing  through  a  prism 
is  always  bent  toward  the  base.  If  the  eye  is  placed  at  K,  the 
source  of  light  will  appear  to  be  at  Lr.  The  position  of  any 
object  seen  through  a  prism  is  apparently  moved  toward 
the  refracting  angle,  which  is  the  angle  formed  by  the  inter- 
section of  the  two  faces  under  consideration. 

If  L  is  raised,  the  refracted  ray  DPI  is  bent  nearer  the  base  and 
the  angle  which  it  makes  with  the  normal  to  the  side  AC  is  increased. 
When  it  reaches  the  value  42°  the  critical  angle  of  the  glass  is 
reached  and  the  ray  is  totally  reflected  within  the  glass  and  emerges 
from  the  prism  through  the  side  EC. 

The  angle  of  deviation  is  the  angle  which  the  incident  and  emergent 
rays  form  with  each  other.  In  Fig.  487  it  is  the  angle  KNO.  This 
angle  varies  with  the  refracting  angle  of  the  prism,  the  index  of 
refraction  of  the  medium,  and  the  angle  of  incidence.  There  is  for 
every  prism  a  minimum  angle  of  deviation,  and  this  is  obtained  when 
the  angles  of  incidence  and  emergence  are  equal. 

519.  Lenses.  —  A  lens  consists  of  a  transparent  body 
bounded  by  two  surfaces,  one  or  both  of  which  are  curved. 
The  curved  surfaces  are  usually  spherical.  There  are  six 
forms  of  lenses  in  common  use,  which  may  be  classified  in 
two  groups  of  three  each : 


1.  Double  convex 

2.  Plano-convex 


Converging    lenses.     Thicker    in 


~  .  the  middle  than  at  the  edge. 

6.  Converging  meniscus 


4.  Double  concave 

5.  Plano-concave 


Diverging  lenses.     Thinner  in  the 


n    T^.         .  middle  than  at  the  edge, 

b.  Diverging  meniscus 


Rev. 


466 


LIGHT 


15 


FIG.  488 

These  lenses  may  be  considered  as  being  formed  as  follows : 

1.  Intersection  of  two  spheres. 

2.  Intersection  of  plane  and  sphere. 

3.  Intersection  of  small  sphere  by  large  sphere. 

4.  Intersection  of  cylinder  by  two  spheres. 

5.  Intersection  of  cylinder  by  plane  and  sphere. 

6.  Intersection  of  cylinder  by  a  small  and  a  large  sphere. 

520.  Center  of  Curvature ;  Principal  Axis ;  Optical  Center. 
—  The  centers  of  the  spheres  whose  surfaces  bound  a  lens  are 

its  centers  of  curvature,  as  C  and 
C'  (Fig.  489).  The  straight  line 
passing  through  these  centers  is 
the  principal  axis  of  the  lens.  In 
FlG-489  piano  lenses  the  principal  axis 

is  a  line  passing  through  the  center  of  curvature  of  the  curved 
surface,  and  normal  to  the  plane  surface.  The  optical 
center  of  a  lens  is  that  point  through  which  a  ray  of  light 
passes  with  practically  no  change  in  its  direction.  In  a 
double  convex  lens  having  the  same  curvature  for  both  sides, 
it  is  the  center  of  the  figure.  In  piano  lenses  it  is  at  the 
intersection  of  the  curved  surface  and  the  principal  axis. 


REFRACTION  OF  LIGHT 


467 


Any  ray  which  passes  through  the  optical  center,  but  does 
not  pass  through  the  center  of  curvature,  is  a  secondary  axis, 
as  HO  in  Fig.  489. 


FIG.  490 

521.  The  Path  of  a  Ray  through  a  Lens.  —  Suppose  the  ray 
to  come  from  the  point  P  on  the  principal  axis  and  to  strike 
a  crown-glass  lens  at  the  point  A  (Fig.  490).     The  direction 
AB  through  the  lens  may  be  found  as  follows : 

Describe  from  A  as  a  center  two  arcs  of  circles  with  radii 
that  are  to  each  other  as  3  :  2  (f  being  the  index  of  refraction 
of 'the  lens).  From  E,  the  intersection  of  the  ray  with  the 
inner  arc  DE,  draw  a  line  parallel  to  the  normal  DA,  and 
from  H,  where  the  parallel  intersects  the  outer  arc,  draw 
HA  and  prolong  it  to  B. 

In  a  similar  way  we  can  determine  the  direction,  BK, 
that  the  ray  will  take  on  emerging  from  the  lens. 

522.  The  Foci  of  Convex  Lenses.  —  The  positions  of  the 
luminous  point  for  which  we  may  determine  foci  in  convex 
lenses  are  similar  to  those  considered  for  concave  mirrors. 
To  determine  the  focus  of  any  point,  two  rays  only  are 
needed.     The  principal  axis  or  a  secondary  axis  is  taken  for 
one  of  these  rays. 


468 


LIGHT 


(a)  When  the  Luminous  Point  is  at  an  Infinite  Distance. 
—  In  this  case  the  incident  rays  are  parallel,  and  if  we  take 

the  index  of  refraction  as  f , 
the  focus 
center   of 


is  very  near  the 
curvature  for  a 
double  convex  lens,  and  at 
twice  that  distance  for  a 
plano-convex  lens.  This  is  the  principal  focus,  and  its  dis- 
tance from  the  lens  is  the  focal  length  of  the  lens. 

(b)  When  the   Luminous   Point   is   at   a  Finite  Distance 
More  than  Twice  the  Focal  Length.  —  If  the  path  of  the  ray 
PA  (Fig.  492)  is  constructed,  it  will  be  found  to  intersect  the 
principal  axis  at  P',  between  Cf  and  twice  the  focal  length. 

(c)  When  the  Luminous  Point  is  at  Twice  the  Focal  Length. 

—  A  construction  will  show  that  the  focus  is  also  at  twice 
the  focal  length  on  the  other  side  of  the  lens. 

(d)  When  the  Luminous  Point  is  at  Less  than  Twice  and 
More    than    Once 

the  Focal  Length. 

—  This    is    the 
converse    of    (6), 
as    is    shown    in 
Fig.  492,  since  if 

the  luminous  point  is  P',  its  focus  will  be  P. 

(e)  When  the  Luminous  Point  is  at  the  Principal  Focus. 

—  This  is  the  converse  of  (a),  and  the  emergent  rays  will 
be  parallel  to  the  principal  axis. 

(f)  When  the   Luminous   Point  is  between  the   Principal 
Focus  and  the  Lens.  —  In  this  case  the  rays  will  emerge  as 
divergent  rays,  and  the  focus  will  be  virtual,  on  the  same  side 
of  the  lens  as  the  luminous  point,  and  farther  away  from  the 
lens. 


FIG.  492 


REFRACTION   OF  LIGHT 


469 


FIG.  493 


Converging  lenses  render  parallel  rays  converging,  increase 
the  convergence  of  converging  rays,  and  decrease  the  divergence 
of  diverging  rays,  or  render  them  parallel 
or  converging. 

Demonstration.  —  Figure  493  shows  how 
the  focus  of  parallel  rays  can  be  found  by 
the  use  of  the  optical  disk. 

523.  The  Foci  of  Concave  Lenses,  —  (a) 
When  the  Incident  Rays   are  Parallel.  — 
In   this  case  the  rays  emerge  as  diver- 
gent rays    (Fig.  494),   and   the  focus  is  virtual.      In  the 
double  concave  lens  of  crown  glass  the  focus  is  pr.actically 

at  the  center  of  curvature; 
in  the  plano-concave  of 
crown  glass,  at  twice  that 
distance  from  the  lens. 

(6)  When  the  Incident 
Rays  are  Diverging. — In  this 
case  a  construction  will  show 
that  the  emergent  rays  are  more  diverging,  and  that  the 
virtual  focus  is  nearer  the  lens  than  in  case  (a). 

(c)  When  the  Incident  Rays  are  Converging.  —  In  this 
case  the  rays  are  rendered  less  converging,  parallel,  or  di- 
verging, and  the  position  and  kind  of  focus, 
if  any,  will  depend  upon  the  amount  of 
convergence  in  the  incident  rays. 

Diverging  lenses  render  parallel  rays 
diverging,  increaw—lhe  divergence  of  di- 
verging rays,  and  decrease  the  convergence 
of  converging  rays,  or  render  them  parallel 
or  diverging.  FIG.  495 


FIG.  494 


470  LIGHT 

Demonstration.  —  Figure  495  represents  the  paths  of  parallel 
rays  on  passing  through  a  double  concave  lens.  The  focal  length 
of  the  lens  can  be  found  by  prolonging  the  diverging  rays  back  until 
they  meet. 

524.  The  Formation  of  Images  by  Lenses.  —  Demonstration. 

—  Take  a  convex  lens,  a  candle,  and  a  screen  into  a  dark  room.  Ar- 
range them  in  line  as  in  Fig.  496, 
and  by  varying  the  relative  dis- 
tances study  the  images  of  the 
candle  formed  on  the  screen  by 
the  lens.  Since  the  image  of  an 
object  is  made  up  of  the  foci 
FIG.  496  of  aii  its  points,  verify  the  po- 

sitions given  for  these  foci  in  §  522. 

525.  Formula  for  Convex  Lenses.  —  The  relative  positions 
of  an  object  and  its  image  formed  by  a  convex  lens  can 
be  determined  if  the  principal  focal  length  is  known,  and 
vice  versa.     The  formula,  like  that  for  concave  mirrors,  is, 

''  .       •  '  l  =  i+i  :\:i-    '   (62) 

in  which  F  is  the  focal  length,  D0  the  distance  of  the  point 
P  from  the  lens,  and  Z)»  the  distance  of  its  image  from  the 
lens.  If  we  let  S0  represent  the  length  or  diameter  of  the 
object,  and  St  that  of  the  image,  then  a  simple  geometrical 
construction  shows  that  S0 :  St  =  D0:  D<. 

526.  Geometrical  Construction  of  Images.  —  The  image 
which  any  lens  will  give  of  an  object  can  be  constructed 
with  great  accuracy.     To  do  this  two  rays  only  are  needed, 
from  each  end  of  the  object.     These  rays  are  the  secondary 
axis,  which  will  pass  through  the  optical  center  of  the  lens, 
and  a  ray  parallel  to  the  principal  axis,  which,  after  passing 


REFRACTION  OF  LIGHT 


471 


through  the  lens,  will  pass  through  its  principal  focus.  The 
image  of  the  arrow  AB  (Fig.  497)  formed  by  the  lens  D  will 
be  A'B'.  The  parallel  ray  AG,  passing  through  the  lens  in 
the- direction  GH,  will  then  pass  through  C",  and  its  intersec- 


tion with  the  ray  AO  continued  will  locate  the  image  of  A 
at  the  point  A'.  The  image  of  B  can  be  found  in  the  same 
way.  From  a  consideration  of  the  triangles  ABO  and  A'B'O 

•4.  •  j.u  4.  Size  of  image       Distance  of  image 

it  is  seen  that  — fe    =  — —     6  . 

oize  or  object        Distance  or  object 

527.  Spherical  Aberration.  —  In  order  that  the  results 
mentioned  in  the  preceding  discussion  on  lenses  may  be 
obtained  experimen- 
tally the  lenses  must 
be  thin  and  the  aper- 
ture small.  If  a  thick 
con  vex  spherical  lens  is 
used,  the  rays  that  pass 
through  it  near  the 
edge  do  not  focus  at 
the  same  point  as  those 
that  pass  through  near 
the  middle  of  the  lens. 
This  can  be  shown  by  construction  as  in  Fig.  498.  The  rays 
LA  come  to  a  focus  at  P,  and  only  those  rays  quite  near 


D' 


FIG.  498 


472  LIGHT 

the  center  focus  at  C.  The  effect  of  this  is  to  make  the 
outside  of  the  image  indistinct  when  the  center  is  distinct, 
and  vice  versa.  This  defect  may  be  remedied  by  using  a 
diaphragm  with  a  hole  in  it,  in  front  of  the  lens,  as  DD'. 
This  makes  the  image  more  distinct,  but  as  it  cuts  off  the 
light  from  the  outside,  the  image  is  not  so  bright. 

Questions 

1.  Suppose  P  to  be  a  luminous  point  at  the  bottom  of  a  dish  filled 
with  water  to  the  line  A  B.     Construct  the  paths  of  the  rays  PC,  PD, 

and  so  on,  making  angles  of 
10°,  20°,  30°,  and  so  on,  with 
the  normal  PN.  Trace  as 
many  of  these  paths  as  will 
strike  on  the  surface  A  B.  Let 
AB  be  10  in.  long  and  the 
water  6  in.  deep. 

2.  Suppose  you  place  a 
block  of  crown  glass  2  in. 
thick  upon  a  point  P  on  the 

FlG-499  table.      Construct  the  paths 

of  rays  passing  from  P  at  the  same  angles  as  in  problem  1. 

3.  Explain  why  the  amount  of  light  reflected  from  a  diamond  is 
greater  than  that  from  a  piece  of  glass  cut  in  the  same  shape. 

4.  Why  does  an  oar  placed  in  the  water  appear  bent  ? 

5.  Why  is  there  a  difference  between  the  apparent  diameters  of 
the  full  moon  when  it  is  rising  and  when  it  is  well  up  in  the  sky? 

6.  Why  does  a  vertical  straight  line,  when  looked  at  in  a  slanting 
direction  through  a  piece  of  ordinary  window  glass,  appear  to  be  full 
of  short  bends,  while  if  it  is  looked  at  through  a  piece  of  plate  glass  it 
appears  straight? 

7.  Prove  that  a  ray  of  light  passing  through  a  prism   is  bent 
toward  the  base. 

8.  Construct  the  paths  of  rays  emerging  from  a  double  convex 
lens  when  the  luminous  point  is  between  the  principal  focus  and  the 
lens. 


DISPERSION  AND   POLARIZATION  473 

9.  Construct  the  paths  of  rays  emerging  from  a  double  concave 
lens  when  the  incident  rays  are  diverging. 

10.  The  radius  of  curvature  of  each  surface  of  a  double  convex 
lens  is  3  ft.  Construct  the  image  it  forms  of  an  arrow  4  ft.  from  the 
lens. 

Problems 

1.  The  distance  of  the  object  is   18  in.  from  a  converging 
lens  and  the  distance  of  the  image   is  6  in.     What  is  _the  focal 
length  of  the  lens? 

2.  Suppose  that  using  the  same  lens  as  in  problem   1,  the 
image  is  found  to  be  at  the  same  distance  from  the  lens  as  the  object. 
What  is  the  distance  ? 

3.  A  reading  glass  has  a  focal  length  of  3  in.     How  far  from 
the  glass  will  it  form  the  image  of  a  lamp  4  ft.  away? 

4.  What  is  the  height  of  the  image  in  problem  3,  if  the  lamp 
is  3  in.  high? 

5.  When  the  image  of  an  object  24  in.  from  a  convex  lens  is 
thrown  upon  a  screen  at  a  distance  of  6  in.  from  it,  what  is  the  focal 
length  of  the  lens?     Wliat  are  the  relative  lengths  of  image  and 
object? 

6.  Find  the  focus  of  a  point  30  cm.  from  a  convex  lens  when  the 
focal  length  is  20  cm. 


IV.     DISPERSION  AND   POLARIZATION 

528.  Color  is  a  property  of   light  that  depends  on  its 
wave   length.     Red  light,   for   instance,   consists  of   ether 
vibrations  with  a  wave  length  of  about  0.0007  mm.,  while 
vibrations  with  a  wave  length  of  0.0004  mm.  produce  the 
sensation  of  violet  light. 

529.  The  Dispersion  of  Light.  —  Demonstration. — Take  a 
prism  into  a  dark  room  and  hold  it  in  front  of  a  horizontal  slit  hi -a 
shutter.     When  a  beam  of  sunlight  passes  through  the  prism,  it  is 
not  only  refracted,  but  separated  into  a  band  of  colors  on  the  oppo- 
site wall. 


474 


LIGHT 


FIG.  500 


This  dispersion  is  due  to  the  fact  that  the  index  of  refrac- 
tion in  a  glass  prism  varies  with  the  wave  length  of  the  light. 

The  spectrum  formed  is 
called  the  solar  spectrum, 
and  consists  of  a  series  of 
colors  passing  impercep- 
tibly from  violet,  which 
is  refracted  the  most, 
through  indigo,  blue, 
green,  yellow,  and  orange, 
to  red,  which  is  refracted  the  least. 

Demonstration.  —  Paste  two  narrow  bands  of  paper,  one  violet 
and  one  red,  upon  a  black  card,  and  look  at  them  through  a  prism. 
It  will  be  seen  that  the  red  rays  are  refracted  less  than  the  violet. 

530.  Recomposition  of  White  Light.  —  Since  the  spectrum 
is  formed  by  the  unequal  dispersion  of  white  light,  it  is 
possible  to  reproduce  white  light  by 
bringing  all  the  spectrum  colors  to 
one  place.  This  can  be  done  by 
using  a  second  prism  reversed,  a 
concave  mirror,  or  a  convex  lens. 


_  ..  a   ,  .  FIG.  501 

Demonstration.  —  Set  up  a  prism  in  a 

dark  room  and  let  the  sunlight  strike  it  through  a  slit  in  the  shutter. 

Let  the  spectrum  fall  upon  a  second  prism  which  is  reversed.  The 

spectrum  colors  being  brought 
together  will  produce  a  brilliant 
white  line. 


531.  Chromatic  Aberration. 

—  Demonstration.  —  Place  a  large 
double  convex  lens  perpendicular 
to  the  sun's  rays  (Fig.  502).  If  a 
screen  is  placed  at  S,  a  picture  of 


FIG.  502 


DISPERSION  AND  POLARIZATION  475 

the  sun  will  be  formed  having  an  outer  fringe  of  red,  but  if  the 
screen  is  placed  in  the  position  S'  the  fringe  will  be  violet. 

This  effect,  which  is  quite  common  in  single  lenses,  is 
called  chromatic  aberration,  and  is  due  to  the  unequal  re- 
fraction of  the  different  colors. 

532.  The  Achromatic  Lens.  —  Achromatism,  or  the  forma- 
tion of  images  without  colored  fringes,  is  secured  by  combin- 
ing a  plano-concave  lens  of  flint  glass  with  a  double 

convex  lens  of  crown  glass.  These  are  of  such  cur- 
vatures that  the  dispersion  of  one  is  neutralized  by 
that  of  the  other,  while  the  refraction  is  retained. 
The  refraction  of  the  combination  is  less,  however, 
than  that  of  the  double  convex  lens  alone.  F10- 503 

533.  The    Rainbow.  —  One    of    the    most    familiar    and 
striking  results  of  refraction  and  dispersion  in  nature  is  seen 
in  the  rainbow.     Whenever  rain  is  falling  and  the  sun  is 
shining  upon  it,  from  a  point  not  too  high  in  the  heavens, 
an  observer  standing  with  his  back  to  the  sun  will  see  one 
and  sometimes  two  of  these  brilliant  bows. 

The  inner  or  primary  bow  is  composed  of  the  spectrum 
colors  in  their  order,  the  red  being  on  the  outside  and  the 
violet  on  the  inside.  The  outer  or  secondary  bow  is  com- 
posed of  the  same  colors,  but  in  inverse  order. 

534.  The  Primary  Bow.  —  When  a  beam  of  sunlight  L 
strikes  upon  a  raindrop  at  A  (Fig.  504),  the  light  that  passes 
into  the  drop  is  refracted  at  A  and  dispersion  begins  at  the 
same  place,  so  that  when  the  light  strikes  the  back  of  the 
drop  it  is  as  a  spectrum,  with  the  red  ray  above  on  account 
of  its  refraction  being  the  least.     At  RV  part  of  the  light 
passes  out  of  the  drop,  but  part  is  reflected.     Since  the  angle 


476 


LIGHT 


of  incidence  ARO  is  greater  than  the  angle  AVO,  the  angle 

of  reflection  ORR'  must  be  greater  than  the  angle  OFF',  and 

for  this  reason  the 
rays  will  cross  at 
B  and  emerge  (in 
part)  from  the 
drop  at  Rf  and 
V  in  the  direc- 
tions R'R"  and 
F'F".  The  other 
spectrum  colors 
will  be  refracted 
in  regular  order  be- 
tween R"  and  V" . 
The  angle  of  in- 

FIG  504  cidence  at  which 

these  results  are 

obtained  is  such  that  the  red  ray  leaves  the  drop  at  an  angle 

of  42°   to  the  direction  of 

the  entering  ray,   and  the 

violet  ray  at  an  angle   of 

nearly  40°.     Hence  the  red 

ray  is  seen  at  an  angle  of 

42°  and   the  violet   at   an 

angle  of  about  40°  to  a  line 

drawn    from   the    observer 


DISPERSION  AND   POLARIZATION  477 

directly  away  from  the  sun.  Since  the  angle  for  the  red 
ray  is  greater  than  for  the  violet,  it  is  evident  that  if  the 
eye  is  placed  at  E  (Fig.  505)  the  different  colors  will  be 
seen  reflected  from  different  drops,  and 
that  the  drop  giving  the  red  ray  will  be 
higher  than  the  others.  This  explains 
why  the  red  is  on  the  outside  of  the  pri- 
mary bow. 

Demonstration.  —  By  using  a  thick  cylinder 
of  glass  with  the  optical  disk,  the  path  of  a  ray 
similar  to  that  which  forms  the  primary  bow  in  a 
raindrop  can  be  traced  as  represented  in  Fig.  506.  FIG.  506 

535.  The  Secondary  Bow.  —  The  sun's  rays  striking  on 
the  lower  side  of  the  raindrop  at  A  (Fig.  507)  will  be  (in  part) 
refracted  and  dispersed  to  VR,  and  then  after  two  reflections 


FIG.  507 

part  of  them  will  emerge  from  the  drop,  the  red  at  an  angle 
of  51°  and  the  violet  at  an  angle  of  54°  to  the  direction  of  the 
entering  ray.  This  means  that  the  eye  will  receive  the  violet 
ray  from  a  higher  elevation  than  the  red  ray,  and  hence 
that  the  violet  will  be  on  the  outside  of  the  secondary  bow. 

536.  Why  the  Rainbow  is  Circular.  —  Since  the  raindrop 
is  a  sphere,  the  red  rays  of  the  primary  bow  are  sent  off  in 


478 


LIGHT 


the  form  of  a  cone  having  the  drop  at  its  vertex  and  making 
an  angle  of  42°  with  the  axis  of  the  cone.     The  red  ray, 

therefore,  can  be  seen,  from 
different  drops,  in  any  di- 
rection that  makes  an  angle 
of  42°  with  the  axis  of  the 
bow,  that  is,  with  the  line 
that  passes  through  the 
sun  and  the  eye  of  the  ob- 
server; and  hence  its  form 
will  be  circular.  In  Fig. 
508  the  sun  is  supposed  to 


E 


FIG.  508 


be  at  the  horizon. 


537.  The  Color  of  Opaque  Bodies  under  white  light  is 
determined  by  their  relative  powers  of  absorbing  and  reflect- 
ing vibrations  of  certain  wave  lengths.  A  body  that  ab- 
sorbs all  the  colors  except  red,  reflects  that  color  and  is  red. 

Demonstrations.  — Paste  a  strip  of  white  paper  upon  a  black  card 
and,  holdingit  in  the  sunlight,  examine  it  by  looking  through  a  prism. 


FIG.  509 

The  edges  of  the  paper  will  give  the  spectrum  colors.  Examine  in 
the  same  way  strips  of  red  and  blue  paper,  and  the  spectrum  in  each 
case  will  give  only  the  color  that  the  paper  reflects. 

Paste  a  strip  of  white  paper,  10  in.  long  and  |  in.  wide,  on  a  black 
card.  Paste,  at  right  angles  to  this,  pieces  f  in.  wide  and  2  in. 
long.  Place  a  prism  as  in  Fig.  509,  and  examine  the  strips.  The 


DISPERSION  AND  POLARIZATION  479 

spectra  of  the  narrow  strips  into  which  we  may  suppose  the  long 
strip  to  be  divided  will  overlap  and  give  white  light  except  at  the 
ends,  one  end  being  red  and  the  other  violet.  The  spectrum  of  each 
narrow  line  will  be  a  complete  spectrum. 

If  the  color  that  a  body  reflects  is  red,  it  will  not  appear 
red  unless  the  light  that  shines  upon  it  has  red  in  it. 

Demonstration.  —  Take  slips  of  differently  colored  paper  into  a 
dark  room  and  examine  them  under  the  light  from  a  photographer's 
lamp  giving  a  ruby  red  light,  or  under  the  yellow  light  from  a  candle 
upon  which  some  salt  has  been  sprinkled. 

This  demonstration  shows  the  importance  of  selecting 
colors  under  the  same  light  as  that  in  which  they  are  to  be 
used.  A  color  that  is  exactly  suitable  by  daylight  may  have 
an  entirely  different  appearance  by  gaslight. 

An  artificial  light  is  better  adapted  for  all  purposes  when 
the  quality  of  its  light  approaches  that  of  sunlight.  Most 
artificial  lights  have  a  greater  proportion  of  yellow  in  them 
than  daylight  has.  The  colors  of  the  decorations  used  in  a 
room  should  be  determined  in  a  great  measure  by  the  color 
of  its  illumination. 

538.  The  Color  of  Transparent  Bodies,  viewed  by  trans- 
mitted light,  depends  upon  the   color  that  they  transmit. 
If  a  body  transmits  all  colors  equally,  it  is  colorless.     If  it 
transmits  one  color  only,  —  yellow,  for  example,  —  then  it 
will  have  that  color;  but  if  it  transmits  several,  its  color 
will  be  that  which  results  from  combining  the  transmitted 
colors  in  the  relative  amounts  in  which  they  are  transmitted. 

539.  Newton's  Disk.  —  Sir  Isaac  Newton  used  a  method 
of  combining   colors   that  depends   upon   the  principle   of 
persistence  of  vision  in  the  eye.     If  a  cardboard  disk  is  painted 
red  on  one  sector  and  yellow  on  the  other,  as  in  A  (Fig.  510), 


480 


LIGHT 


FIG.  510 


and  if  it  is  then  rapidly  rotated  on  an  axis  passing  through 

the  middle  of  the  disk,  the 
color  will  appear  to  the 
eye  to  be  orange.  This  is 
purely  a  physiological  re- 
sult, the  red  sensation  fol- 
lowing the  yellow  sensation 
so  quickly  that  the  result 
is  a  combination  of  the  two.  If  violet  and  red  are  used  in- 
stead of  yellow  and  red,  the  result  will  be  purple.  Combina- 
tions of  any  colors,  in  any  proportions,  can  be  made  by  having 
a  disk  of  each  color  slit  radially,  as  B  in  Fig.  510,  so  that  they 
can  be  slipped  over  one  another  while  on  the  axis. 

540.  Complementary  Colors.  —  If  blue  and  orange  are 
used  in  the  right  proportions  in  Newton's  disk,  the  resulting 
effect  will  be  practically  white.  Two  colors  which,  added 
together,  produce  white,  are 
called  complementary  colors. 

A  chart  like  that  shown  in 
Fig.  511  is  convenient  for 
showing  complementary 
colors.  It  is  so  arranged  that 
the  combination  of  any  two 
colors  opposite  will  produce 
white,  and  the  combination 
of  any  two  spectrum  colors 
will  produce  the  color  be-  FlG- 5n 

tween  them;  e.g.,  red  and  yellow  will  produce  orange.  Yel- 
low and  blue  in  varying  proportions  will  produce  varying 
shades  of  green;  and  red  and  blue  in  varying  proportions  will 
produce  varying  shades  of  purple  and  violet. 


DISPERSION   AND   POLARIZATION  481 

The  three-color  process  is  a  method  of  making  colored 
pictures  of  almost  any  tint  or  shade  of  color  by  using  only 
three  colored  inks  in  printing.  Photographic  negatives  of  a 
colored  picture  are  made  through  screens  of  red,  blue,  and 
yellow.  Copper  plates  are  engraved  from  these  and  each  is 
inked  with  its  color.  By  printing  these,  one  over  the  other, 
in  exact  register,  very  pleasing  results  are  obtained.  (The 
frontispiece  of  this  book  is  printed  by  this  process.) 

541.  Camouflage.  —  The    protective    coloring    of    quail, 
zebras,  and  many  other  animals  makes  them  difficult  to 
distinguish  from  their  native  landscapes.   In  the  World  War 
a  similar  principle  was  extensively  applied  in  "  camouflage" — 
the  painting  or  screening  of  cannon,  ships,  and  other  things  to 
conceal  them  from  observation  by  the  enemy.  In  the  case  of 
merchant  ships,  however,  it  was  found  more  feasible  to  use  the 
deceptive  "  dazzle  "  system  of  camouflage.    (See  frontispiece.) 

542.  The  Spectroscope  is  an  instrument  for  the  produc- 
tion and  study  of  the  spectra  from  different  sources.     It 
has  three  essential 

parts,  shown  in 
diagram  in  Fig. 
512. 

The  collimator 
C  is  provided  with 

a  slit  at  the  end 

.,       ,.  ,,  FIG.  512 

nearest   the   light 

L,  and  a  lens  so  arranged  that  the  light  will  pass  from  the 
collimator  to  the  prism  in  parallel  lines.  The  prism  P 
is  fixed  in  such  a  position  that  the  refracted  beam  passes 
through  it  and  emerges  in  the  direction  of  PT.  The  tele- 
scope T  is  movable,  arid  can  be  focused  on  any  ray  that 
emerges  from  the  prism.  A  general  view  of  one  form  of  the 
instrument  is  shown  in  Fig.  513. 

Rev. 


482  LIGHT 

543.  Spectrum  Analysis.  —  The  kind  of  spectrum  that  is 
given  by  any  source  of  light  depends  upon  the  physical 

condition  of  the  source. 
There  are  three  kinds  of 
spectra :  the  continuous 
spectrum,  the  bright  line 
spectrum,  and  the  absorp- 
tion or  dark  line  spectrum. 


544.  First  Law  of  the 
Spectrum.  —  Demonstra- 
tion.—  Examine  the  flame 
of  a  candle  by  the  spectro- 
scope, and  it  will  be  seen  to 
be  continuous  from  the  red 
FIG.  513.— Spectroscope  en(j  to  the  violet,  passing 

through  all  the  intermediate  colors  by  imperceptible  gradations. 

LAW  I.  When  the  source  of  light  is  an  incandescent  solid, 
liquid,  or  dense  gas,  the  spectrum  is  continuous. 

The  continuous  spectrum  in  the  above  demonstration  is 
the  spectrum  of  incandescent  solid  particles  of  carbon 
from  the  candle.  The  same  kind  of  spectrum  is  obtained 
from  a  lamp  or  gaslight. 

545.  Second  Law  of  the  Spectrum.  —  Demonstration. — Dip  a 

platinum  wire  in  a  solution  of  salt  and  hold  it  in  a  nonluminous  Bun- 
sen  flame ;  or  soak  a  strip  of  cloth  or  asbestos  in  salt  water  and  wind 
it  around  the  top  of  a  Bunsen  burner.  Examine  the  flame  with  the 
spectroscope,  and  instead  of  a  continuous  spectrum,  a  bright  yellow 
band  will  be  seen  in  the  middle  of  the  place  occupied  by  the  yellow 
of  the  continuous  spectrum. 

This  yellow  band  is  called  the  sodium  line,  or  D  line, 
and  on  being  closely  studied  is  seen  to  be  made  up  of  two 
narrow  bright  lines  with  a  dark  band  between  them. 


DISPERSION  AND  POLARIZATION  483 

LAW  II.  Incandescent  gases,  not  under  great  pressure, 
give  a  spectrum  made  up  of  bright  colored  lines  on  a  dark 
background. 

Each  line  has  a  definite  position  in  the  spectrum,  and  is 
characteristic  of  the  substance  which  produces  it. 

546.  Third  Law  of  the  Spectrum. — Demonstration. — Exam- 
ine sunlight  by  the  spectroscope,  and  the  colored  spectrum  will  be 
seen  to  be  crossed  by  a  series  of  dark  lines.     Moisten  a  platinum 
wire  with  a  solution  of  salt  and  hold  it  in  a  Bunsen  flame  in  front  of 
the  slit.     One  of  the  dark  lines,  the  D  line,  will  be  made  darker. 
Shut  out  the  sunlight  and  examine  the  sodium  flame  alone,  and  the 
D  line  will  show  in  the  same  place  as  a  bright  yellow  line. 

We  see  in  this  demonstration  that  the  passage  of  sunlight 
through  sodium  vapor  —  itself  capable  of  giving  a  bright 
line  —  intensifies  the  dark  line  in  the  solar  spectrum.  The 
fact  that  this  dark  line  is  in  the  same  place  as  the  bright  line 
does  not  mean  that  there  is  no  sodium  in  the  sun,  but  instead 
means  that  the  sodium  vapor  in  the  sun's  atmosphere  absorbs 
the  light  of  the  same  wave  length  as  that  given  out  by  incan- 
descent sodium,  and  makes  this  part  of  the  spectrum  look 
dark  in  comparison  with  the  rest  of  it.  Such  spectra  are 
called  absorption  spectra. 

LAW  III.  The  vapor  of  any  substance  will  absorb  the  light 
given  out  by  that  substance  in  a  state  of  incandescence. 

Absorption  spectra  can  be  shown  by  holding  in  front  of  the  slit  of 
a  spectroscope  a  test  tube  containing  a  solution  of  potassium  per- 
manganate when  the  solar  spectrum  is  being  observed.  It  will  then 
be  seen  that  the  spectrum  is  crossed  by  a  number  of  dark  bands.  The 
vapors  of  barium  and  strontium  will  produce  similar  results. 

547.  Fraunhofer  Lines.  —  The  dark  lines  described  above 
are  called  the  Fraunhofer  lines,  and  on  account  of  their  inva- 


484 


LIGHT 


riable  position  are  used  as  standards  of  wave  length.  A  care- 
ful comparison  of  the  position  of  these  lines  with  the  bright 
line  spectra  of  iron,  copper,  silver,  zinc,  sodium,  and  many 
other  elements  shows  that  they  have  exactly  the  same  wave 
lengths,  and  hence  it  is  concluded  that  these  elements  exist 


A     B     C       D 


F 


G 


II 


FIG.  514 


in  the  atmosphere  of  the  sun  in  a  state  of  vapor.  The  posi- 
tions of  the  most  prominent  of  the  Fraunhofer  lines  are 
shown  in  Fig.  514,  in  which  the  violet  end  of  the  spectrum  is 
at  the  right. 


LINE 

COLOR 

WAVE  LENGTH  IN  MAI. 

A 

Dark  Red 

0.0007594 

B 

Red 

0.0006870 

C 

Orange 

0.0006563 

Di 

Yellow 

0.0005896 

D2 

Yellow 

0.0005890 

E! 

Light  Green 

0.0005270 

F 

Blue 

0.0004861 

G 

Dark  Blue 

0.0004308 

H 

Violet 

0.0003968 

The  above  table  gives  the  wave  lengths  of  some  of  the 
dark  lines  of  the  spectrum.  There  are  parts  of  the  visible 
spectrum  in  the  red  end  that  have  longer  wave  lengths  than 
the  A  line,  as  well  as  parts  in  the  violet  that  have  shorter 
wave  lengths  than  the  H  line. 

548.  The  Invisible  Spectrum.  —  The  visible  spectrum  is 
by  no  means  the  limit  of  the  dispersion  secured  by  the 


DISPERSION  AND  POLARIZATION  485 

prism.  Beyond  the  red  are  a  series  of  longer  waves  that 
can  easily  be  detected  as  heat  rays,  while  beyond  the  violet 
are  shorter  waves  that  have  great  chemical  activity,  and 
are  called  the  chemical  or  actinic  rays. 

Demonstration. — Cut  a  piece  of  photographic  printing  paper 
into  strips  and  pin  them  end  to  end  upon  the  wall  of  a  dark  room  so 
as  to  form  a  long  strip.  By  means  of  a  prism  throw  the  solar  spec- 
trum upon  the  middle  of  the  strip,  which  should  extend  a  third  of  its 
length  beyond  each  end  of  the  spectrum.  Mark  the  position  of 
every  color  and  the  end  of  the  visible  spectrum.  After  a  short 
exposure  notice  that  the  greatest  effect  on  the  paper  is  at  the  violet 
end  of  the  spectrum  or  just  beyond  it,  and  that  at  the  red  end  there 
is  practically  no  change. 

549.  Doppler's  Principle  Applied  to  Light  Waves. —  The 
position  of  the  dark  lines  of  the  spectrum  is  invariable  only 
when  the  distance  between  the  source  of  light  and  the  ob- 
server is  fixed.  If  this  distance  is  regularly  diminishing, 
the  wave  length  corresponding  to  a  given  line  diminishes, 
and  if  it  is  increasing,  the  wave  length  increases. 

If  the  spectrum  of  a  star  is  examined,  and  it  is  found  that 
the  C  line,  for  instance,  is  located  at  the  right  of  the  position 
of  that  line  in  the  solar  ^  c  v 

spectrum,  as  the  lighter 
line  in  Fig.  515,  the 
explanation  is  that  the 
star  is  moving  toward  us  and  thus  shortening  the  wave 
length  that  produces  the  line.  If  the  displacement  is 
toward  the  red  end  of  the  spectrum,  then  the  star  is  reced- 
ing from  us.  Since  the  velocity  of  the  star  determines  the 
amount  of  this  displacement,  a  measurement  of  this  amount 
can  be  used  as  a  basis  for  calculating  the  velocity  of  the 
star's  motion. 


FIG.  515 


486  LIGHT 

550.  Interference.  —  We  have  already  seen  the   results 
of  interference  in  sound  waves.     Two  waves  may  meet  in 
such  a  way  as  to  strengthen  each  other  or  to  neutralize  each 
other.     Similar  phenomena  occur  in  light. 

Demonstration.  —  Against  a  piece  of  plate  glass  press  the  curved 
side  of  a  plano-convex  lens  of  great  focal  length.  On  looking  at  the 
upper  surface  of  the  lens  at  an  angle,  a  series  of  concentric  circles 
will  be  seen,  each  one  of  which  will  be  made  up  of  the  colors  of  the 
spectrum.  If  a  sheet  of  red  glass  is  placed  between  the  lens  and  the 
light,  so  that  light  of  that  color  alone  falls  upon  the  lens,  the  rings 
will  be  alternate  dark  and  red  bands.  Two  strips  of  plate  glass 
separated  at  one  end  by  a  sheet  of  paper  and  pinched  together  at  the 
other  will  also  show  interference  bands. 

The  rings  shown  by  the  lens  are  called  Newton's  rings. 
The  colors  seen  on  looking  at  a  thin  film  of  oil  on  water, 
a  soap  bubble,  or  a  crack  in  a  piece  of  ice,  are  other  ex- 
amples of  interference. 

551.  Explanation  of  Newton's  Rings.  —  When  light  strikes 
the  lens  the  refracted  ray  is  partly  reflected  at  A  and  its  phase 

is  changed.1  Some 
other  refracted  ray 
will  be  reflected  from 
B  without  change  of 
phase,  and  will  pass 
into  the  air  in  the 

— — —    same  path  as  the  first, 

^ B  I    CD.      If  the  distance 

FIG.  516  A  7>  • 

A  B  is  a  quarter  wave 

length,  the  reflected  rays  are  in  the  same  phase  and  give 
light ;  but  if  it  is  a  half  wave  length  the  reflected  rays  are  in 

1  A  change  of  phase  of  half  a  wave  length  takes  place  whenever 
light  is  reflected  back  into  a  dense  medium  instead  of  passing  into 
a  rarer  one. 


DISPERSION  AND  POLARIZATION  487 

opposite  phases  and  there  is  interference  or  darkness.  As  the 
space  between  the  curved  surface  of  the  lens  and  the  plane 
glass  increases  gradually,  there  is  a  distance  that  corresponds 
to  a  quarter  wave  length  for  every  color  of  the  spectrum. 

552.  Diffraction.  —  Demonstrations.  —  Expose  a  photographic 
dry  plate  to  daylight.  Develop  it  and  fix  it.  Wash  it  thoroughly  and 
dry  it.  With  a  fine  needle  or  the  point  of  a  knife  blade  draw  a  series 
of  parallel  lines  through  the  film  to  the  glass.  Hold  this  plate  close 
to  the  eye  and  look  through  it  at  the  flame  of  a  candle.  There  will 
be  seen  brilliant  spectrum  colors  extending  on  either  side  of  the 
flame.  ;  '•• 

On  one  half  of  the  plate  used  above,  draw  two  sets  of  parallel  lines 
at  right  angles  to  each  other,  dividing  the  film  into  small  squares. 
Look  through  this  at  an  arc  or  incandescent  light,  and  fine  lines  of 
spectra  will  be  seen  to  extend  at  right  angles  from  the  light. 

A  fine  silk  handkerchief  gives  a  good  effect  when  looked 
through,  especially  when  the  light  examined  is  an  arc  light. 
A  plate  of  glass  upon  which  a  little  lycopodium  powder 
has  been  sprinkled  gives  a  series  of  beautiful  rainbow  effects 
when  a  candle  or  any  bright  light  is  seen  through  it.  The 
cause  of  these  phenomena  is  that  rays  of  light  on  passing 
through  a  narrow  slit  spread  out  into  a  diverging  band,  or 
are  diffracted;  and  if  the  edges  of  the  slit  are  near  each 
other,  interference  takes  place  and  gives  colored  fringes. 

The  diffraction  grating  consists  of  from  10,000  to  20,000 
parallel  lines  to  the  inch,  ruled  on  glass  or  on  speculum 
metal.  If  on  the  former,  the  light  passes  through,  if  on 
the  latter,  it  is  reflected  from  the  polished  and  ruled  surface. 
Spectra  of  wide  dispersion  can  be  obtained  from  such  gratings, 
and  they  are  used  in  place  of  the  prism  in  spectroscopic  work. 
The  spectrum  given  by  the  grating  is  called  the  normal 
spectrum,  since  in  it  the  distribution  of  the  different  wave 
lengths  is  uniform. 


488 


LIGHT 


553.  Polarized  Light.  —  The  vibrations  of  the  ether  that 
produce  a  ray  of  light  are  transverse  vibrations  in  every 

direction.  Figure  517 
may  be  taken  to  rep- 
resent a  cross  section 
of  a  ray  of  light, 
showing  vibrations  in 
a  few  of  these  direc- 
tions. If  all  the  vi- 
brations were  parallel 
transversely,  as  in  Fig.  518,  then  the  ray  would  be  a  ray  of 
plane  polarized  light.  Polarized  light  affects  the  eye  just  like 
ordinary  light,  but  it  presents  certain  very  interesting  phe- 
nomena, some  of  which  are  shown  in  the  following  pages. 

The  crystal  tourmaline  has  the  property  of  permitting 
vibrations  in  only  one  plane  to  emerge  from 
it ;    that  is,  it  polarizes  light. 


FIG.  518 


FIG.  519 


Demonstrations.  —  Place  two  tourmaline  crys- 
tals one  over  the  other  and  parallel  to  each  other. 
The  light  that  passes  through  one  will  pass  through 
the  other.  Now  turn  one  of  them  until  it  crosses 
tlie  other  at  right  angles,  as  in  Fig.  519,  and  no  light  at  all  passes 
through  the  crossed  portion.  The  action  is  as  though  each  let 
through  only  those  vibrations  which  are  parallel  to  its  length. 
Now  put  between  the  tourmalines  a  piece  of  quartz  or  Iceland  spar, 
and  on  turning  one  of  the  tourmalines,  brilliant  color  effects  are 
observed.  The  effect  of  the  quartz,  then,  must  be  to  turn  the  plane 
of  polarization  and  to  enable  a  part  of  the  light  to  pass  through  the 
second  tourmaline,  producing  the  color  effects  by  partial  interference 
of  the  polarized  rays. 

Lay  a  sheet  of  black  paper  upon  the  table.  Over  this  lay  a  sheet 
of  glass  G  (Fig.  520).  Cut  out  ten  or  twelve  pieces  of  thin  glass, 
and  holding  them  as  at  A  in  the  figure,  look  through  them  at  a 
piece  of  mica  M  laid  upon  the  glass  sheet.  Hold  the  thin  glasses  at 


DISPERSION  AND   POLARIZATION 


489 


various  angles  and  elevations,  and  determine  the  position  in  which 
the  most  brilliant  effects  are  produced.    The  same  results  are  ob- 


FIG.  521 


FIG.  520 

tained  if  the  eye  is  placed  below  the  glasses  in  such  a  position  that 
the  polarized  ray  is  reflected  from  B. 

554.  Double  Refraction.  —  If  a  crystal  of  Iceland  spar 
AB  (Fig.  521)  is  placed  upon  a  sheet  of  paper  on  which  there 
is  a  black  dot,  the  eye  placed  above 
the  spar  will  see  two  dots,  one  a  short 
distance  from  the  other  and  appar- 
ently above  the  surface  of  the  paper. 
This  separation  of  the  light  into  two 
rays  shows  that  light  passes  through 
the  crystal  more  rapidly  in  one  direction  than  in  the  other 
and  is  called  double  refraction. 

Two  rays  from  each  point  reach  the  eye  by  different  paths : 
one  of  them  obeys  the  ordinary  laws  of  refraction,  and  is 
called  the  ordinary  ray;  the  other  does  not  obey  these  laws, 
and  is  called  the  extraordinary  ray.  Another  peculiarity  of 
these  rays  is  that  they  are  polarized. 

If  a  crystal  of  Iceland  spar  is  cut  along  the  diagonal  AB 
and  then  cemented  together  again  with  Canada  balsam,  it 
has  the  property  of  permitting  only  the  extraordinary  ray  to 
emerge.  This  arrangement  is  called  a  Nicol's  prism,  and  is 
much  used  in  the  study  of  polarized  light. 


490 


LIGHT 


555.  The  Polariscope.  —  The  study  of  substances  by  polar- 
ized light  has  become  a  matter  of  great  importance  on  account 

of  its  use  in  the  detection 
of  adulteration ;  the  sub- 
stitution of  grape  sugar 
for  cane  sugar,  for  ex- 
ample. A  simple  polari- 
scope  (Fig.  522)  serves  to 
demonstrate  many  of  the 
phenomena  of  polarized 
light  nearly  as  well  as 
more  elaborate  apparatus. 
The  base  AB  supports  a  vertical  ground-glass  plate  C.  A 
piece  of  black  glass,  or  a  glass  plate  over  a  sheet  of  black 
paper r  is  laid  on  the  base  at  D.  An  arm  E  is  fixed  to  the 
base  at  an  angle  of  about  35°.-  K  supports  a  Nicol's  prism 
and  L  the  object  to  be  studied.  Mica  cut  in  different  thick- 
nesses gives  beautiful  color  effects.  The  strained  condition 
of  the  glass  in  a  pressed  bottle  stopper  can  be  detected  by  the 
appearance  of  dark  spots  as  the  Nicol's  prism  is  rotated. 


FIG.  522.  —  Polariscope 


Questions 

1.  Make  a  drawing  of  a  prism,  the  refractive  angle  A  of  which  is 
60°,  and  trace  the  path  of  a  ray  from  L  as  it  passes  through  and 
out  of  the  prism.     Using  the  same  incident  ray  L,  increase  the  angle 
A  by  10°  successively,  and  show  the 

change  in  the  emerging  ray  until  it  no 
longer  emerges  from  the  side  AC. 
Where  does  the  ray  emerge? 

2.  What  shape  of  rainbow  might  it 
be  possible  to  see  from  a  balloon? 

3.  If,  in  examining  with  a  spectro- 
scope the  light  from  a  distant  body,  FIG.  523 


OPTICAL  INSTRUMENTS  491 

you  should  find  the  spectrum  continuous,  what  conclusion  would 
you  draw? 

4.  The  velocity  of  light  has  been  given  as  300,000  km.  per  second. 
Take  the  wave  length  of  the  red  (B)  line  from  the  table  in  §547, 
and  find  how  many  waves  of  that  color  strike  the  eye  per  second. 

6.  In  observing  the  spectrum  of  a  star,  the  D  line  was  found  to 
be  displaced  toward  the  violet  end  of  the  spectrum.  What  is  the 
meaning  of  the  displacement  ? 

6.  In  pressing  two  pieces  of  glass  together  in  a  photographic 
printing  frame,  a  number  of  groups  of  colored  lines  sometimes 
appear.     What  is  the  explanation  ? 

7.  The  light  used  in  a  photographic  dark  room  is  a  red  light. 
Why? 

V.   OPTICAL  INSTRUMENTS 

556.  The   Simple   Microscope  is   merely  a   convex  lens, 
usually  of  short  focal  length.     The  object  is  placed  between 
the  principal  focus  and       ^^^ 

the  lens,  and  the  image 

is  virtual,  upright,  and 

larger  than  the  object. 

If  the  object  AB  (Fig. 

524)  is  placed  as  shown, 

the  position  of  the      ^j^  FIG.  524 

image  of  the  point  A 

is  determined  by  the  intersection,  at  A','ot  aFf  and  AO. 

Bf  is  found  in  a  similar  way,  and  the  positions  of  these 

two  points  determine  the  position  of  the  whole  image.     The 

distance  from  the  eye  to  the  image  is  the  distance  of  distinct 

vision  and  varies  with  different  eyes. 

557.  The  Compound  Microscope  (Figs.  525  and  526).  — 
The  simplest  form  of  the  compound  microscope  consists  of 
two  converging  lenses :  an  object  glass  0  and  an  eyepiece  E. 


492 


LIGHT 


The  distance  between  these  is  so  arranged  that  the  object 
glass  forms  a  real,  enlarged,  inverted  image  of  the  object 
between  the  eyepiece  and  its  focus.  The  function  of  the 


FIG.  525.  —  Diagram  of  a  Compound  Microscope 

eyepiece  is  to  enlarge  this  image,  so  that  the  eye  sees  the 
enlarged  and  inverted  image  at  ab. 

558.  The  Astronomical  Telescope.  —  The  ordinary  astro- 
nomical telescope  (refracting)  is  much  like  the  compound 
microscope  in  principle.     But  while  both  lenses  magnify 
in  the  microscope,  owing  to  the  nearness  of  the  object  to  the 
object  glass,  the  eyepiece  alone  magnifies  in  the  telescope. 
This  is  due  to  the  fact  that  the  object  is  at  a  distance,  and  the 
image  formed  by  the  object  glass  is  nearly  at  its  principal 
focus  and  very  small. 

559.  The  Terrestrial  Telescope.  —  The  image  given  by 
the  astronomical  telescope  is  an  inverted  one.     The  invert- 
ing of  the  image  is  not  very  objectionable  when  one  is  looking 


493 


494 


LIGHT 


at  the  heavenly  bodies;  but  in  a  telescope  to  be  used  on 
objects  on  the  surface  of  the  earth,  it  is  more  convenient  to 
have  the  image  upright.  This  result  is  secured  usually  by 
putting  two  converging  lenses,  at  proper  distances,  between 
the  object  glass  and  the  eyepiece. 

560.  Galileo's  Telescope ;  the  Opera  Glass.  —  The  sim- 
plest, and  also  the  oldest  form  of  telescope  is  Galileo's  tel- 
escope. This  has  but 
two  lenses ;  namely, 
a  convex  object  glass, 
and  a  concave 
piece  (Fig.  527). 


FIG'.  527.  —  Galileo's  Telescope 


eye- 
The 

eyepiece  is  placed  be- 
tween the  object  glass 
and  the  image  formed 
by  it.  Being  concave,  the  eyepiece  causes  the  rays  to  di- 
verge and  appear  to  the  eye  to  come  from  ab,  which  thus 
forms  an  enlarged  upright  image. 
Opera  glasses  consist  of  a  pair  of 
these  telescopes. 

561.  The  Prism  Binocular.  — The 

insertion  of  the  two  converging  lenses 
between  the  object  glass  and  the  eye- 
piece insures  an  upright  image  in  the 
terrestrial  telescope,  but  increases  the 
absorption  of  light.  The  use  of  a 
pair  of  Porro  prisms  gives  an  upright 
image  and  shortens  the  tube  of  the 
instrument  so  that  it  can  be  used,  in 
the  form  of  a  binocular,  as  an  opera 

i  TT  ^o  FIG.  528.  —  Prism 

glass.    Figure  528  represents  such  an  Binocular 


OPTICAL  INSTRUMENTS 


495 


opera  glass,  half  in  cross  section.  The  arrow  represents  the 
path  of  a  ray  of  light  through  the  instrument.  This  ray  is 
totally  reflected  from  the  inner  surfaces  of  the  prisms  four 
times. 

562.  The  Optical  Lantern  is  used  for  the  purpose  of  throw- 
ing an  enlarged  picture  of  a  lantern  slide  upon  a  screen.     The 


FIG.  529.  —  Optical  Lantern 

essential  parts  are  some  brilliant  source  of  light,  a  condensing 
lens  (7,  formed  of  two  plano-convex  lenses  with  curved  sur- 
faces toward  each  other,  a  glass  lantern  slide  S,  upon  which  is 
the  picture  to  be  enlarged,  and  a  projecting  lens  P,  a  combina- 
tion of  lenses  for  enlarging  the  picture.  The  electric  arc  is 
the  best  artificial  light  for  projection,  since  the  light  is  intense 
and  its  size  is  small.  The  lime  light,  in  which  a  cylinder  of 
lime  is  raised  to  incandescence  by  the  heat  from  an  oxyhydro- 
gen  blowpipe,  is  a  good  light.  In  cases  where  the  lantern  is 
to  be  used  in  a  small  room,  an  incandescent  lamp  with  a 
spiral  filament  is  satisfactory.  Such  lamps  are  made  to  give 
from  50  to  100  candle  power,  and  are  most  convenient 
wherever  there  is  an  incandescent  circuit. 
Book  illustrations  or  opaque  objects  can  be  used  for  projec- 


496 


LIGHT 


tion  instead  of  lantern  slides  by  directing  the  light  from  an  arc 
light  or  other  brilliant  source  against  the  picture.     An  image 


FIG.  530 


FIG.  531 


of  this  picture  is  thrown  upon  the  screen  by  a  projecting  lens. 
Some  lanterns,  like  the  balopticon,  are  so  arranged  that  both 

lantern  slides  and  pictures  can  be  used.  Figure  530  shows 

the  use  of  two  mirrors 
with  the  lantern 
slide.  When  a  pic- 
ture is  to  be  pro- 
jected, the  lower 
mirror  is  raised  and 
the  light  falls  directly 
upon  the  picture  as 
in  Fig.  531.  The 
complete  apparatus 
is  shown  in  Fig.  532. 

The   moving-picture 
FIG.  532.  —  Balopticon  ,  .  f 

lantern  used  to  throw  upon  a  screen  in  rapid  succession  a  series  of 
pictures  taken  at  intervals  of  a  small  fraction  of  a  second.  Sixteen 
pictures  per  second  is  the  usual  number.  The  retina  of  the  eye  re- 


OPTICAL  INSTRUMENTS 


497 


tains  each  image  until  the  next  is  presented  and  links  them  to- 
gether to  show  continuous  motion.     (Figs.  533,  538.) 


FIG.  533.  —  Moving-picture  Machine 

563.  The  Camera,  used  in  photography,  consists  of  a  light- 
tight  box  having  at  one  end  an  achromatic  lens  and  at  the 
other  a  ground-glass 
plate  and  a  space  in 
which  a  plateholder 
containing  a  sensi- 
tized plate  can  be 
placed.  In  order  to 
regulate  the  amount 
of  light  passing 
through  the  lens  and 
to  increase  the  dis- 
tinctness by  cutting  off  the  outside  rays,  the  lens  is  pro- 
vided with  a  series  of  diaphragms  with  different-sized  open- 
ings. The  camera  is  so  constructed  that  the  distance 

Rev. 


Fro.  534.  —  Camera 


498 


LIGHT 


OPTICAL  INSTRUMENTS  499 

between  its  ends  can  be  varied.  By  making  this  the 
proper  distance  the  image  is  brought  to  a  focus  on  the  ground 
glass,  then  the  sensitized  plate  is  put  in  its  place,  and  the 
exposure  is  made. 

The  plate  is  afterward  developed  by  means  of  certain  chemicals. 
This  process  reduces  the  silver  salts  in  the  film  to  a  metallic  con- 
dition, forming  a  dark  layer  wherever  the  light  has  acted.  The  salt 
that  has  not  been  acted  upon  by  the  light  is  dissolved  out  by  putting 
the  plate  in  a  solution  of  hyposulphite  of  sodium,  after  which  the 
plate  is  washed  and  dried.  The  plate  is  now  a  negative  (Fig.  535), 
and  prints  can  be  made  from  it  upon  sensitized  paper  (Fig.  536). 

Figure  538  shows  a  moving  picture  camera ;  Fig.  539,  a  machine 
for  sending  a  photograph  a  long  distance  by  wire. 

564.  The  Eye  as  an  Optical  Instrument.  —  The  eye  is  a 
minute  camera,  with  dark  chamber,  lens,  diaphragm,  and 


screen  upon  which  the  image  is  formed.  The  sclerotic  coat 
S  (Fig.  518)  forms  the  wall  of  the  dark  chamber,  and  is 
extended  in  front  as  a  transparent  coat  C  called  the  cornea. 
The  lens  L  of  the  eye  is  formed  of  an  elastic,  transparent 
substance,  and  is-  called  the  crystalline  lens.  Extending 
over  the  front  of  the  lens  is  a  colored  curtain  or  diaphragm, 
the  iris,  which  determines  the  color  of  the  eye,  and  which  has 


500  LIGHT 

a  circular  opening  in  the  center  called  the  pupil.  The  image 
of  an  object  is  brought  to  a  focus  upon  the  inner  lining  r  of  the 
eye  called  the  retina,  from  which  the  sensation  of  sight  is 
carried  to  the  brain  by  means  of  the  optic  nerve.  The  yellow 
spot  Y  is  the  most  sensitive  part  of  the  retina,  and,  since  it  is 
on  the  axis  of  the  eye,  is  the  spot  on  which  is  formed  the  image 
of  the  point  at  which  the  eye  looks  directly. 

We  have  seen  that  in  the  camera  the  distance  between 
the  lens  and  the  ground  glass  is  changed  in  order  to  bring 
a  given  object  to  a  focus.  The  distance  between  the  crys- 
talline lens  and  the  retina,  however,  is  a  fixed  distance, 
and  the  focus  is  obtained  by  a  change  in  the  curvature  of 
the  front  of  the  lens,  thus  changing  its  focal  length.  This 
change  of  curvature  of  the  lens  to  change  its  focus  for  ob- 
jects at  different  distances  is  called  accommodation. 

565.  The  Blind  Spot. —At  the  inner  side  of  each  eye 
where  the  optic  nerve  enters  there  is  a  blind  spot.     This 
can  be  readily  proved  as  follows :    Close  the  left  eye  and 
look  steadily  at  the  cross  below  with  the  right.     A  position 
can  be  found  in  which,  while  you  look  steadily  at  the  cross, 

+  O 

the  circle  will  disappear.  When  this  position  is  found  the 
circle  may  be  brought  into  view  by  moving  the  book  either 
nearer  to  the  eye  or  farther  away. 

566.  The  Adaptability  of  the  Retina  of  the  eye  as  a  screen 
for  receiving  the  image  formed  —  because  of  its  concave 
shape  —  is  shown  as  follows  : 

Demonstration.  —  Fix  a  convex  lens  in  the  shutter  of  a  dark 
room.  Place  a  white  paper  screen  in  such  a  position  that  the 
middle  of  the  image  of  the  landscape  will  be  in  focus.  The  edges 


OPTICAL  INSTRUMENTS 


501 


FIG.  538.  —  MOVING  PICTURE  STUDIO  WITH  A  CAMERA  IN  ACTION 

Exposures  in  rapid  succession  are  made  by  simple  mechanism  operated  by  a  small 
crank.  Perfect  illumination  is  secured  by  light  from  above,  combined  with  banks  of  mer- 
cury vapor  lamps  (§  469)  at  the  side. 


502 


LIGHT 


^Illrlll 
L?i.s|§i| 

«g£«c-fi"S 

*3*~-B*-v«* 
ls«s.sIS|.e 

!JP 

~»  :~    *— 


C  2.S  i-«^  ^H  S 
^^.1^l^§«     « 

l^gtPsI 


o    a  5  9  8  ®S-5  a 

2  &§||5|1b| 
2  S-fBj^^fiiJ 
§  »l|5lgs-|^ 

;ill«igils 

|a|2i|5eg 


3 


OPTICAL  INSTRUMENTS 


503 


will  be  blurred  and  indistinct.  Now  bend  the  screen  into  the  form 
of  a  section  of  the  surface  of  an  upright  cylinder,  and  all  parts  of  the 
picture  on  a  horizontal  line  will  be  equally  distinct.  Turn  the  screen 
to  other  positions  and  observe  the  effect. 

567.  Light  and  Illumination.  —  The  most  important  use 
of  artificial  light  is  the  illumination  of  interiors.  For  interior 
illumination  both  the  incandescent 
electric  lamp,  preferably  the  tung- 
sten, and  the  incandescent  mantle 
gas  lamp,  provide  light  units  that 
combine  convenience  and  efficiency 
to  a  high  degree. 

There  are  three  systems  of  distri- 
bution that  are  used- with  both  gas 
and  electric  lighting,  the  direct,  the 
indirect,  and  the  semi-indirect. 

The  direct  system  is  one  in  which 
the  light  from  the  lamp  shines  di- 
rectly upon  the  area  lighted,  either 
with  or  without  the  help  of  reflect- 
ing shades.  This  system  gives  the 
maximum  amount  of  light  for  a 
given  expenditure  of  energy,  but  is 
objectionable  on  account  of  the  glare 
of  the  light  which  either  comes  di- 
rectly from  the  lamp  or  is  reflected  from  polished  surfaces. 
This  objection  can  be  partially  overcome  by  the  use  of 
frosted  lamps  or  translucent  globes,  when  it  becomes  a  modi- 
fied direct  system. 

The  indirect  system  is  one  in  which  the  lamps  are  placed 
.within  two  or  three  feet  of  the  ceiling  while  opaque,  bowl- 
shaped  reflectors  are -placed  below  the  lamps.  The  inner 


Opaque  bowl 


Interior  reflectors 
FIG.  540.  —  Indirect  System  , 


504 


LIGHT 


surface  of  the  bowls  is  made  of  a  highly  reflecting  material 
and  thus  the  light  from  the  lamp  is  reflected  from  the  ceiling, 
from  which  it  is  diffused  throughout  the  room.  Less  light 
is  thrown  on  a  given  surface,  a  table  top,  for  example,  for  the 
same  expenditure  of  energy,  than  in  the  direct  system,  but  as 
the  eyes  are  not  tired  by  the  direct  glare  of  the  light,  objects 
are  seen  equally  well  under  the  reduced  intensity.  This 
system  does  away  with  the  harsh  shadows  of  the  direct  sys- 
tem, the  only  shadows  formed  being  soft  and  pleasing.  One 
form  of  bowl  with  interior  reflectors  is  shown  in  Fig.  540. 
The  semi-indirect  system  is  one  which  is  intended  to  com- 


FIG.  541.  —  Distribution  of  Light  by  a  Shade 

bine  the  advantages  of  both  the  direct  and  indirect  systems 
and  to  avoid  the  objectionable  features  of  each.  The  method 
adopted  is  to  reflect  a  part  of  the  light  to  the  ceiling  for  general 
illumination  and  to  direct  the  rest  downward  either  directly 
or  through  translucent  screens. 

This  system  has  the  advantages  of  lighting  a  limited  area 
well  without  concentrating  all  the  light  upon  it  and  leaving 
the  rest  of  the  room  unlighted. 

In  order  to  light  a  limited  area,  such  as  the  top  of  a  desk 
or  table,  reflecting  shades  are  used.  These  are  of  various 
types,  depending  upon  the  character  of  distribution  desired, 


OPTICAL   INSTRUMENTS 


505 


Those  that  light  but  a  small  area  are  called  "  concentrating  " 
shades,  while  the  "  distributing  "  shade  spreads  the  light  over 
a  much  larger  area. 

Figure  541  shows  one  type  of  shade  and  the  change  in  the 


FIG.  542.  —  Section  of  Lighthouse  Lenses  arranged  to  throw  Parallel  Rays 
in  Four  Directions 

distribution  made  by  its  use.  The  dotted  curve  gives  the 
distribution  of  light  from  the  lamp  without  a  shade,  the 
radial  distance  of  the  curve  at  any  point  from  the  center 
giving  the  candle  power  of  the  lamp  in  that  direction.  The 
full-line  curve  shows  the  distribution  when  the  shade  is  used, 
the  greater  part  of  the  light  being  thrown  downward, 


CHAPTER  XI 
INVISIBLE  RADIATIONS 

568.  Hertz  Waves.  —  We  have  already  seen  that  a  radi- 
ometer can  be  set  in  motion  by  invisible  heat  rays  (§  274), 
and  that  the  sensitized  film  on  photographic  paper  is  affected 
by  invisible  radiations  of  shorter  wave  length  than  those 
of  violet  light  (§  548).  We  are  now  to  consider  invisible 
radiations  set  up  by  electrical  means.  If  the  discharge  of 
a  Leyden  jar  is  sent  through  a  metallic  circuit  and  across  a 
short  air  gap,  it  will  set  up  a  like  discharge  in  the  air  gap  in 
the  circuit  of  a  second  similar  jar,  provided  the  circuits  are 
parallel  and  the  areas  of  the  circuits  are  the  same.  This 
electrical  resonance  is  analogous  to  the  setting  of  a  tuning  fork 
in  motion  by  the  vibrations  of  a  similar  fork  (§  210).  If 
the  forks  do  not  vibrate  at  the  same  rate,  the  second  fork  will 
not  be  put  in  vibration,  and  if  the  area  of  the  second  circuit 
is  changed,  no  spark  will  appear  in  the  second  air  gap.  The 
fork  is  put  in  motion  by  waves  of  air;  but  electrical  reso- 
nance is  caused  by  ether  waves  set  up  by  the  spark  in  the 
first  circuit. 

We  have  seen  that  the  electric  spark  discharge  or  a  Leyden 
jar  is  oscillatory  (§  370).  If  the  image  of  the  spark  is  ob- 
served in  a  mirror  revolving  at  high  speed,  it  is  seen  to  be 
a  succession  of  flashes  following  each  other  at  extremely 
short  intervals. 

506 


HERTZ  WAVES 


507 


The  velocity  of  the  ether  waves  set  up  by  electrical  oscilla- 
tions was  first  determined  by  Heinrich  Hertz  in  1888,  hence 
they  are  known  as  the  Hertz  waves.  This  velocity  is  the 
same  as  that  of  light,  300,000  km.  per  second.  Hertz  found 
that  there  were  10,000,000  oscillations  per  second,  hence 
the  wave  length  is  30  m.  By  reducing  the  size  of  the  Leyden 
jar  and  the  length  of  the  circuit,  and  letting  the  discharge 
take  place  between  two  balls,  the  wave  length  can  be  made 
much  shorter  and  the  number  of  oscillations  per  second  much 
greater. 

Silver  or  nickel  filings  placed  between  two  metal  disks 
in  a  glass  tube  have  an  extremely  high  resistance.  On  the 
passage  of  an  ether  wave  sent  out  by  a  Leyden  jar  spark, 
the  filings  cohere  and  offer  little  resistance.  Marconi  used 
this  coherer  as  a  detector  of  ether  waves  in  wireless  telegraphy, 
by  putting  it  in  a  local  circuit,  containing  a  sounder  or  bell, 
which  gave  a.  signal  on  every  passage  of  a  wave  from  the 
sending  station. 

The  sending  station  (Fig.  543)  of  a  .wireless  telegraph  sys- 
tem will,  in  general,  include :  a  transformer,  A,  or  a  Ruhm- 
korff  coil,  the  second- 
ary of  which  is  con- 
nected to  the  spark  _ 
gap,  B,  the  condenser 
C,  and  the  primary 
helix  D  of  an  induc- 
tion coil.  The  termi- 
nals of  the  spark  gap 

B      are     of      zinc     and        FIG.  543.  —  Diagram  of  a  Sending  Station 

usually  inclosed  in  a  glass  globe  to  reduce  the  noise  of  the 
discharge.  The  secondary  helix  E  is  grounded  at  one  end 
and  terminates  at  the  other  end  in  the  antenna  F,  a  wire  or 


508  INVISIBLE   RADIATIONS 

group  of  wires  going  high  into  the  air.  On  closing  the  key 
K,  a  spark  jumps  across  B  and  by  properly  adjusting  the 
size  of  the  condenser  (7,  the  turns  of  wire  in  D  and  E,  and 
the  distance  between  D  and  E  with  a  given  area  and  eleva- 
tion of  the  antenna,  the  two  circuits  BCD  and  EF  may  be 
so  tuned  that  a  maximum  of  electrical  wave  energy  may  be 
radiated  into  space  from  F. 

These  electric  waves,  traveling  in  all  directions  with  the 
speed  of  light,  may  be  roughly  likened  to  the  waves  set  up 
in  still  water  when  a  stone  is  thrown  into  it.  Gradually 
lessening  in  amplitude,  they  may  be 
perceived  in  any  direction  at  a  dis- 
tance which  depends  upon  the  sen- 
sitiveness of  the  detector. 

The  receiving  station  for  wireless 
work  (Fig.  544)  consists  of  the  an- 
tenna F,  connected  to  one  end  of 
a  coil  H,  the  other  end  of  which  is 
FIG  544 -Diagram  of  a      grounded;   a  coil  /,  movable  with 

Receiving  Station 

respect  to  H ;  a  detector  J;  a  con- 
denser C,  and  a  telephone  receiver. 

The  feeble  electric  waves  reaching  the  antenna  F,  many 
million  times  per  second,  may  be  heard  in  the  telephone, 
upon  properly  adjusting  H  to  F  and  I  to  H,  as  a  distinct 
musical  tone  every  time  the  key  K  in  the  sending  station 
is  closed.  The  very  rapid  oscillations  of  the  electric  waves 
cannot  be  detected  by  the  unaided  telephone  receiver  because 
the  diaphragm  cannot  vibrate  fast  enough.  Hence  it  is  neces- 
sary that  the  detector  be  so  constructed  that  the  train  of  waves 
sent  out  each  time  the  sending  key  is  closed  shall  be  received 
as  an  individual  signal  the  length  of  which  depends  upon 
the  length  of  time  the  sending  key  is  in  contact. 


WIRELESS   TELEGRAPHY 


509 


Many  devices  have  been  developed  that  will  do  this  with 
more  or  less  efficiency.  One  which  combines  sensitiveness 
and  convenience  consists  of  a  contact  between  two  crystals 
or  between  a  metal  and  a  crystal.  Silicon,  zincite,  bornite, 
carborundum,  and  molybdenite  have  been  successfully  used. 
The  action  of  this  type  of  detector  depends  upon  the  fact 
that  the  contact  between  the  crystals  offers  a  much  greater 
resistance  to  the  passage  of  the  current  in  one  direction  than 
in  the  other.  Thus  one  part  of  the  electric  wave  will  produce 
current  through  the  detector  and  the  telephone,  while  that 
part  of  the  wave  which  is  in  the  opposite  direction  will  pro- 
duce no  current  and  is  unheard. 

The  form  of  antenna  used  depends  upon  the  power  of  the 
station.  For  a  small  output  the  straight  vertical  form  is 

generally  sufficient. 
^z  A  flat  top  is  some- 

^^  times  used  with  the 

vertical,  as  in  Fig. 
545.  For  receiving, 
nearly  any  metal 
surface  raised  above 
the  ground  and  in- 
sulated from  it  will 
serve  as  antenna. 
Signals  from  a 
neighboring  send- 
ing station  may  frequently  be  heard  in  the  receiver  of  an 
ordinary  telephone  system,  the  wires  acting  as  antenna  and 
the  house  fuse  block  as  detector. 

The  invention  of  the  audion  for  receiving  wireless  mes- 
sages has  made  possible  the  use  of  a  much  smaller  aerial 
than  that  shown  in  Fig.  545.  The  audion  consists  of  a  glass 


FIG.  545 


510 


INVISIBLE   RADIATIONS 


bulb  that  looks  much  like  an  incandescent  lamp.  It  con- 
tains, besides  a  lamp  filament,  a  thin  metallic  plate  and  a 
wire  grid,  placed  between  the  plate  and  the  filament. 

One  method  of  coupling  the 
audion  to  the  receiving  circuit  is 
shown  in  Fig.  546.  The  coil  an- 
tenna is  from  four  to  six  feet 
across.  Its  sensitivity  is  at  a  maxi- 
mum when  the  direction  of  the 


Coil  Antenna 


Audion 


FlG.   546 

wireless  wave  is  in  the  plane  of  the  coil;  hence,  it  can  be 
used  to  locate  the  direction  of  the  source  of  the  wave  if  it 
is  mounted  on  a  vertical  axis  around  which  it  can  be 
turned. 

A  modified  form  of  the  audion  serves  to  amplify  the  loud- 
ness  of  the  signals.  By  coupling  a  number  of  audions  in 
cascade  arrangement  accurate  and  clear  results  are  obtained 
in  extreme  long  distance  wireless  telephone  transmission, 
such  as  that  in  transoceanic  communication.  The  audion 
is  also,  for  the  physical  investigator,  a  tool  of  the  greatest 


CATHODE  RAYS  511 

delicacy,   applicable   to    investigations  in  many    different 
fields. 

569.  Cathode  Rays.  —  In  considering  the  luminous  effects 
of  the  inductive  discharge  (§  445)  we  saw  that  the  spark  is 
longer  and  much  more  brilliant  in  a 

partial  vacuum  than  in  ordinary  air. 
Professor  William  Crookes  made  an 
extensive  study  of  the  phenomena  of 
electric  discharges  in  high  vacuum 
tubes.  A  high  vacuum  is  one  in  which 
the  gaseous  pressure  is  not  more  than 
one  millionth  of  that  of  the  atmos- 
phere. Figure  547  shows  the  form  of 
tube  with  which  he  studied  the  differ- 
ence between  the  phenomena  when 
high  and  low  vacua  are  used.  If  the 
vacuum  is  low,  the  discharge  shows  a 
curved  band  of  light  from  the  cup- 
shaped  platinum  cathode  to  whichever  FlG'  547—  Crookes  Tube 
wire  is  made  the  -f-  terminal.  If,  however,  the  vacuum 
is  high,  the  discharge  passes  from  the  cathode  directly  across 
the  globe  to  the  opposite  wall,  which  glows  with  a  yellowish 
green  fluorescence. 

A  study  of  the  action  of  the  cathode  rays  (§  570)  leads 
to  the  conclusion  that  they  consist  of  a  stream  of  minute, 
negatively  charged  particles  that  are  projected  from  the 
cathode  in  a  direction  perpendicular  to  its  surface,  with 
a  velocity  about  one  tenth  that  of  light  (Fig.  547). 

570.  Effects  of  the  Cathode  Rays.  —  (a)   The  Mechanical 
Effect.  —  In  the  tube  shown  in  Fig.  548  a  light  wheel  is  made 


512 


INVISIBLE  RADIATIONS 


to  roll  along  the  glass  rails,  either  to  the  left  or  to  the  right, 
depending  on  whether  A  or  B  is  made  the  cathode.  The 

rotation  of   the  wheel   is  caused 
by  the  stream  of   particles   sent 
off  by  the  cathode,  which  strike 
the  vanes  on  the  top  of  the  wheel. 
(6)    The  Heating  Effect.  —  The 
FlG-  548  tube  shown  in  Fig.  549  is  a  focus 

tube  having  a  thin  piece  of  platinum  at  the  focus  of  the 
cup-shaped  cathode.  The  continuous  blows  of  the  re- 
pelled particles  constituting  the  cathode  rays 
cause  this  piece  of  platinum  to  become  red- 
hot. 

(c)   The    Magnetic    Effect.  —  By    using    a 
straight  tube   and  placing   a  strong  electro- 
magnet near   one  side,   as  in  Fig.  550,  it  is 
possible  to  deflect  the  rays  from  their  straight 
path    whenever    an    electric   current    is   sent 
through  the  coil  of  the  electromagnet.     The 
fact  that  the  rays  are  deflected  by  a  mag- 
netic field  proves  that  they  are  made  up  of       FIG.  549 
charged   bodies,   and   the  direction   of    this  deflection   in- 
dicates  the  kind   of   charge  carried. 

(d)  The  Fluorescent  Effect. 
-  The  tube  shown  in  Fig. 
551  contains,  as  the  anode, 
a  cross  of  aluminum  or  mica, 
hinged  to  a  support  at  the 
FlQ-  65°  bottom.     When  a  current  is 

sent  through  the  tube,  the  bombardment  of  the  cathode  rays 
causes  the  glass  walls  of  the  tube  to  glow  with  a  fluorescent 
light  except  where  they  are  protected  by  the  cross,  which 


RONTGEN  RAYS  513 

itself  receives  the  bombardment.  This  shows  the  straight- 
line  path  of  the  particles.  If  now  the  cross  is  suddenly  swung 
down  on  its  hinge  to  the  bottom 
of  the  tube,  the  part  of  the  tube 
that  was  dark  before  will  glow 
more  brightly  than  the  rest. 
This  is  due  to  the  fact  that  the 
fluorescence  fades  out  after  the 
rays  have  been  striking  the  glass 
for  some  time.  The  glass  may  FIG.  551 

be   said  to   possess   a   fluorescent   fatigue. 

571.  The  Rontgen  Rays  or  X-Rays.  —  Certain  luminous 
tubes,  when  the  secondary  current  from  an  induction  coil 
is  passed  through  them,  send  off  rays  that  make  fluores- 
cent  substances  glow  and   affect  the  photographic  plate. 
These  rays  have,  moreover,  the  property  of  passing  through 
many  opaque  substances  as  rays  of  light  pass  through  trans- 
parent substances.     They  proceed  from  that  part  of  the  sur- 
face of  the  tube  upon  which  the  cathode  rays  strike,  and  were 
called  by  Professor  Rontgen,  of  Wiirzburg,  their  discoverer, 
the  X-rays.     Unlike  the  cathode  rays,  they  are  not  affected 
by  a  magnetic  field.     Unlike  light  waves,  they  are  not  re- 
fracted by  lenses  nor  reflected  by  mirrors.     They  may  per- 
haps best  be  described  as  irregular  pulses  set  up  in  the  ether 
as  a  result  of  the  impact  of  the  cathode  rays  upon  the  side 
of  the  tube. 

572.  Radiographs.  —  While  the  X-rays  pass  through  flesh 
with  very  little  difficulty,  the  bones  offer  much  obstruction. 
This  makes  it  possible  to  locate  the  position  of  the  bones  by 
means  of  X-ray  photographs,  or  radiographs  (Fig.  552).     The 

Rev. 


INVISIBLE    RADIATIONS 


FIG.  552. —  Radiograph  of  a  Foot,  showing  a  Broken  Needle 
Embedded  in  the  Flesh 

radiographs  are  of  great  help  to  the  surgeon  in  setting  a 
broken  bone  or  in  locating  a  foreign  body,  as  a  bullet  or 
needle  (Fig.  552) .  They  are  of  great  help  to  dentists  also. 

Radiographs  are  usually  made  as  follows:  A  photographic 
plate  is  inclosed  in  a  plate  holder,  the  object  to  be  radio- 
graphed is  placed  upon  the  cover  of  the  holder,  and  the 
X-rays  are  directed  upon  it,  from  a  tube  only  a  few  inches 
away. 

Several  forms  of  Crookes  tubes  (Section  569)  are  capable 
of  giving  off  the  X-rays.  In  the  forms  called  focus  tubes 
(Fig.  553),  the  cathode  rays  are  brought  to  a  focus  on 
a  platinum  plate  turned  at 
such  an  angle  that  the  rays 
are  sent  out  radially  through 
the  glass.  Devices  are  also 
employed  to  regulate  the  vac- 
uum automatically,  for  other- 
wise it  would  become  higher 
with  use,  until  the  current 
would  no  longer  pass.  FIG.  553  X-ray  Field 


RADIO-ACTIVITY 


515 


573.  The  Fluoroscope,  a  form  of  fluorescent  screen,  was 
devised  by  Edison  in  order  that  he  might  study  the  effect 
of  the  Rontgen  rays  without 

the  use  of  photographic  plates. 
It  consists  of  a  screen  covered 
with  crystals  of  calcium  tung- 
state  and  fixed  to  a  boxlike 
support  with  opaque  sides 
which,  opposite  the  screen,  fit 
so  closely  around  the  eyes 
that  they  cut  off  all  outside 
light.  By  means  of  the  flu- 
oroscope  a  person  may  ex- 
amine,  for  instance,  the  bones  FlG*  554. -Fluoroscope 

of  his  own  hand  by  putting  it  before  the  screen  and  look- 
ing through  the  screen  toward  a  tube  that  is  giving  off 
X-rays. 

574.  Radio-activity.  —  The  study  of  the  X-ray  and  its 
effects  gave  rise  to  the  idea  that  there  was  a  relation  between 
phosphorescence  and  the  X-rays.     In  1896  Becquerel  found 

that  all  the  salts  of  uranium,  both 
those  that  are-  phosphorescent  and 
those  that  are  not,  emit  radiations 
which  affect  the  photographic  plate 
like  the  X-ray  and  pass  through 
thin  sheets  of  metal.  Any  sub- 
stance that  spontaneously  emits  ra- 
diations like  uranium  is  called  radio- 
active, and  is  said  to  possess  radio-activity.  Besides  uranium, 
thorium  and  its  compounds  are  remarkably  radio-active. 
Figure  555  shows  the  effect  produced  upon  a  photographic 


FIG.  555 


516  INVISIBLE  RADIATIONS 

plate  by  the  radiation  from  a  piece  of  gas  mantle  which 
was  placed  upon  the  plate  and  left  in  the  dark  for  five  days. 
The  gas  mantle  contains  thorium. 

Madame  Curie  examined  many  substances  to  determine 
their  radio-activity,  and  she  found  that  pitchblende,  the 
mineral  from  which  uranium  is  obtained,  is  much  more  radio- 
active than  uranium.  She  concluded  that  pitchblende  must 
contain  some  element  more  radio-active  than  uranium,  and 
finally  succeeded  in  separating  from  it  a  minute  quantity,  a 
few  milligrams  per  ton,  of  salts  of  a  new  element  which  she 
called  radium.  Radium  chloride  has  been  obtained  with  a 
radio-activity  one  million  times  as  great  as  that  of  the  mineral 
from  which  it  came. 

Rutherford  has  found  in  the  Becquerel  rays  three  classes 
of  rays  :  The  a-rays  (alpha-rays)  consist  of  positively  charged 
particles,  having  about  twice  the  mass  of  the  hydrogen  atom, 
and  a  velocity  about  one  tenth  that  of  light.  The  /3-rays 
(beta-rays)  are  negatively  charged  particles,  having  about 
yijo-  the  mass  of  the  hydrogen  atom,  and  a  velocity  of  from  0.6 
to  0.96  that  of  light.  They  apparently  differ  from  cathode 
rays  in  velocity  only.  The  7-rays  (gamma-rays)  are  be- 
lieved to  be  pulses  in  the  ether  similar  to  the  X-rays  produced 
in  a  tube  having  a  high  vacuum.  Of  the  three  classes  of 

rays  the  7-rays  have  the  greatest 
penetrating  power  and  the  a-rays 
the  least.  Figure  556  represents 
rays  sent  out  by  a  radio-active 
material,  showing  the  change  in 
direction  caused  by  subjecting 
them  to  a  strong  magnetic  field. 

The  a-rays  are  deflected  little,  the  /3-rays  much,  the  7-rays 
not  at  all. 


IONIZATION  517 

575.  Electrons ;  lonization.  —  When  a  charged  gold-leaf 
electroscope  is  surrounded  with  air  in  normal  condition,  it 
will  retain  its  charge.     As  soon,  however,  as  X-rays  or  the 
radiations  from  radium  fall  upon  it,  it  loses  its  charge  and  the 
leaves  fall  together.     To  explain  this  change  in  the  conduc- 
tivity of  the  air  it  is  necessary  to  consider  the  modern  theory 
of  the  atom.     This  is  that  the  atom  is  a  complex  structure 
consisting  of  minute  negatively  charged  particles  in  rapid 
motion,  connected  with  positively  charged  particles  which  are 
themselves  in  motion.     The  negatively  charged  particles  are 
called  electrons.      The  velocity  with  which  the  «-rays  and 
/3-rays  leave  a  radio-active  material  is  probably  due  to  the 
velocity  which  the  charged  particles  have  within  the  atom, 
and  which  they  retain  as  they  leave  it.     It  is  supposed  that 
the  X-ray  pulses  separate  electrons  from  the  atoms  in  air. 
This  leaves  the  air  a  mixture  of  negatively  charged  electrons 
and  positively  charged  particles,  thus  making  it  a  conductor, 
or  ionizing  it. 

576.  Conclusion.  —  Since    electrons    separate    from    the 
atoms  of  radio-active  substances  it  is  evident  that,  however 
slow  the  process,  there  is  going  on  a  disintegration  or  breaking 
down  of  the  atom.     This  expulsion  from  the  atom  is  accom- 
panied by  the  production  of  such  an  amount  of  heat  that  the 
temperature  of  radium  bromide  is  sometimes  as  much  as  five 
degrees  Centigrade  above  that  of  the  surrounding  air.     In 
order  to  understand  the  significance  of  this  atomic  disintegra- 
tion it  must  be  followed  a  step  farther.     Certain  radio- 
active substances,  as  radium,  actinium,  and  thorium,  emit 
a  substance  like  a  heavy  gas  that  is  endowed  with  temporary 
radio-active  properties.     This  is  called  the  emanation.     If 
kept  for  a  number  of  days,  it  loses  a  large  portion  of  its  radio- 


518  INVISIBLE   RADIATIONS 

activity,  and  on  being  examined  with  the  spectroscope,  shows 
the  well-defined  lines  of  the  element  helium,  which  were  not 
present  when  the  emanation  was  first  formed.  This  seems 
to  indicate  a  change  from  one  element  into  another.  Perhaps 
it  is  rather  an  indication  that  both  these  elements  are  but 
forms  of  a  third  and  possibly  unknown  element. 

To  Dalton  belongs  the  credit  of  giving  the  atom  its  place 
of  honor  as  the  fundamental  unit  of  the  chemist.  It  has 
taken  the  combined  research  of  many  physicists  since 
Dalton's  time  to  establish  the  complicated  structure  of  the 
atom  and  to  show  us  at  least  a  part  of  its  function  in  the 
formation  of  matter. 


APPENDIX 

ANSWERS   TO    NUMERICAL   PROBLEMS 

Page  33.  1.  31.58ft.;  9.63m.  2.  1099.08ft.  3.  169.16m 
4.  163.07m.  5.  157.5  cm.;  47.17  kg.  6.  146.93km.  7.  210m. 

8.  3.62  cu.  m.        9.    165  Ib  ;    74.84  kg.        10.   907.2  kg.         11.   9.84 
long  tons.          12.   8000  liters;  8000  kg.;    17,636.8  Ib.          13.   88.9  kg. 
14.    14,081.5  Ib. 

Pages  67-69.  1.  11.34  mi.  per  hour;  16.63  ft.  per  sec.  2.  65.906 
mi.  per  hour;  96.66  ft.  per  sec.  3.  As  347,976  :  704,000.  4.  163.8 
ft.  per  sec.;  402  ft.;  144.72  ft.  5.  200.8  ft.  per  sec.;  602  ft.;  184.72  ft, 
7.  2250  ft.  8.  5  sec.;  24.505  m.  per  sec.  9.  36.18  ft.  10.  24 
ft.;  12  ft.  per  sec.  11.  196.98  ft.  12.  5,881,200  dynes. 

13.  72.11  Ib.  14.   442.8  ft.          15.   38.09  ft.  per  sec.         16.   6  ft. 

17.  5.76  ft.  from  the  36-lb.  force;  100  Ib.  18     18,48  Ib.;  36.95  Ib. 

19.  11.785  mi.      20.  79.67  ft.  per  min.;  159.35  ft.  per  min.      21.  4  ft.; 
2  ft.  8  in.        22.    54.18  Ib. 

Pages  78-79.  1.  7200  ft.  Ib.  2.  47,040  ft.  Ib.  3.  352  kilo- 
gram-meters. 4.  16  ft.  per  sec.  per  sec.;  3482.6  Ib.  5.  1440ft.  Ib. 
6.  4142  ft.  Ib.;  3534  ft,  Ib.;  608  ft.  Ib.  7.  123.5  H.  P.;  about  92,100 
watts.  8.  14,000  ft.  Ib.;  8000  ft.  Ib.;  14,000  ft.  Ib.  9.  115,200  ft, 
Ib.;  1.16  H.  P.;  115,200  ft.  Ib.  10.  41  min.  11  sec.  11.  320 
H.  P.  12.  11.52  H.  P.  13.  4.77  sec.;  153.43  ft.  per  sec.;  1830 
ft.  Ib. 

Page  89.  1.  7.2;  7.68.  2.  80  Ib.  3.  1.5  ft.;  1.6  ft.  from  cen- 
ter of  10-lb.  ball.  4.  .92  ft.  from  middle  toward  heavier  boy.  5.  3. 
ft.  6.  4.54  cm.  from  weight,  7.  300,000  ft.  Ib.  8.  8482.8  ft.  Ib. 

Page  96.         1.   223.46  cm.  2.    1.108  sec.  3.   99.305  cm. 

4.   99.289cm.        5.   981.82. 

Pages  114-118.       1.   90%.        2.   86.6%.       3.   2.4  in.          5.    7.75 

ft.  to  right  of  F.  acting  upward;  131  Ib.  by  lever  downward  and  136  Ib. 
by  F.   upward.         6.    17.86;    138  Ib.         7.    13.3  1\         8.   41.6  Ib. 

9.  25  Ib.      10.    19;  1425  Ib.      11.   880  Ib.      12.    10.55  Ib.       13.    5.5  in. 

519 


520  APPENDIX 

14.  800  Ib.          15.    104.72  ft.  per  sec.  16.   63.69.  17.   5.5:1. 

18.  20  in.        19.   48.83  Ib.;  640  ft.        20.   550  Ib.;  12  ft.        21.    104 
kg.;  18m.       22.   7; 89. 14 kg.        23.   36 Ib.        24.   916.6 Ib.        25.   598 
Ib.;  1.8  H.  P.         26.   24  H.  P.         27.    1759.3  Ib.         28.   Tf0  in.  per 
sec.;  2.094  in.  per  see.         29.    K  in.  or  1%  in.         30.   22,619.52  Ib.; 
0.398  in.        31.   4.7%.        32.   36%.        33.    12.5%. 

Page  129.        1.   One  half  as  great.         2.   0.04  mm.         3.   418.5  ft. 

Pages  143-146.       1.    13,920  Ib.       2.   5.39  sq.  in.       3.    10,584  Ib. 

4.  90,000  Ib.        5.    17.36  Ib.        6.   35,437.5  Ib.        7.    160  g.;  2176  g. 

8.  63,281.25  Ib.;  63,281.25  Ib.         9.   99.8  Ib.         10.    100,473+  gal.; 
419.73  tons;  846.66  tons;  6250  Ib.        11.   4057.9  Ib.;  15.        12.   6406.25 
Ib.         13.   2.38  kg.         14.  84,375  Ib.         15.   20.83  Ib.         16.   8  ft. 
from  top.         17.   10  ft.  from  top.         18.   480  kg.;  360  kg.;  288  kg. 

19.  8584kg. 

Pages  154-156.  1.  1005.4  cu.  in.;  1580  cu.  in.  2.  187.5  Ib.; 
62.5  Ib.;  43.75  Ib.;  43.75  Ib.  3.  3.84  in.  4.  229.25  Ib.  or  229.2  Ib.*; 
1.328  in.  5.  8.43  ft.  6.  0.96  in.  7.  165.7  tons.  8.  2.35. 

9.  8.6;  8.6.      10.    1.66;  209  g.       11.   21.568  or  21.59.*       12.   2.69  Ib. 
13.    113.59  Ib.   or  113.36  Ib.*  14.    2.61.;  163+  Ib.   per  cu.  ft, 

15.  2  cu.  ft.       16.   3134.4  Ib.;  565.6  Ib.       17.   500  g.       18.   42.9  g.; 
15.7  g.       19.   331.8  cu.  in.       20.   0.772.       21.   0.916.        22.  0.001293 
g.  per  c.c.        23.    1.032.        24.   0.88;  55  Ib.        25.    116  Ib. 

Pages  189-190.  1.  375.7  g.  per  sq.  cm.  2.  50,803.2  Ib.  3.  55 
cu.  ft.  4.  One  fifth.  5.  33.87  ft.  6.  98.6  Ib.  7.  20  cu.  ft. 
8.  5%.  9.  10,584  Ib.  10.  17,733.7  ft.  Ib.  11.  33.77ft. 

12.   8125.23  mm.;  10.79  mm.  13.   20  in.  15.   3.4  atmospheres. 

16.  0.0135  atmosphere.         17.   32.97  ft.         18.   0.68  g.         19.   13.35 
Ib.  per  sq.  in.        20.   67.7  Ib.        21.   336.45  kg. 

Page  202.  1.  1135.2  ft.  or  1136.5  ft.  2.  3389.27  ft.  or  3391.5  ft. 
3.  558.88  ft.  or  559.25  ft.  4.  844.05  ft.  or  844.87  ft.  5.  7.5  sec. 
nearly.  6.  10,692  ft.  or  10,701.9  ft,  7.  2824.4  ft.  or  2826.25  ft. 

8.  3377.7  ft.  or  3379.5  ft.;  16,888  ft.  par  ssc.  or  16,897.5  ft.  per  sec. 

9.  4.3+.        10.    12,491  ft.  nearly  or  12,501.5  ft. 

Page  220.       1.   50   in.         2.   8.52   in.          3.   329.34   m.        4.  2. 

5.  255.        6.    16.        8.   330 +  ;  310  nearly. 


'  Differing  answers  possible  with  different  methods  of  solution,  because  the  weight 
62.5  Ib.  per  cu.  ft.  of  water,  and  the  numbers  in  table  on  p.  150,  are  only  approximate 
values. 


APPENDIX  521 

Page  236.  1.  66.6cm.  3.  75;300.  4.  100; 88.8; 80; 75;  66.6; 
60;  53.3;  50.  5.  12  ft.;  6  ft.  6.  12.8  in.  7.  256.  8.  44.4 
cm.;  64  cm.  9.  0.212  in.;  0.847  in.  or  0.848  in. 

Page  246.  1.  45°.  2.  15°.  3.  77°  F.  4.  -2.7°  C. 
5.  -40°.  6.  36.8°  C.  7.  24.4°  G.  8.  -313.96°  F.  9.  2768°  F. 

10.  9.4°  C. 

Page  280.         1.   0.1045  in.          2.   0.000016.          3.   0.04176  mm. 

4.  1.09  cu.  ft.        5.   3689.2  cu.  ft.        6.   457.2  c.c.         7.    146.25  c.c. 

8.  4.097kg.  9.   57.75°  C.  10.   168°  C.  11.  Air  at  23°  C. 

12.  8.9  g.         '13.   58%.         14.   13.505  g.;   16.881  g.;   between  19°  C. 
and  20°  C. 

Pages  286-287.  1.  17,000.  2.  810.  3.  0.1086.  4.  9.36 
g.  5.  7.52  g.  6.  17.12  g.  7.  36.4°  C.  8.  88.9°  C. 

9.  51.8°  C.  10.   1.77  kg.  11.    12.5  min.  12.    11,520. 

13.  960.       14.    11,066.6  cal.       15.   42  min.  57.6  sec.       16.    131.63  g. 
17.   28,680  cal.        18.    157.89  g.        19.   90,000. 

Page  299.       1.    105,000.         2.    18°  F.         3.   2.78  Ib.        4.   3.21°. 

5.  7068.6  ft.  Ib.;  14,137.2  ft.  Ib.;  1,498,543.2  ft.  Ib.;  45.4  H.  P. 

Page  317.  1.  10,000.  2.  -pole;  240  maxwells.  3.  533.3 
dynes.  4.  2513.28  maxwells.  5.  750  gausses. 

Pages  361-362.  1.  16.87  ohms.  2.  102.52  ohms.  3.  135.26 

ohms.  4.  1.359  amp.  5.  1.177  amp.  6.  0.5  amp.  7.  0.127 

amp.  8.  0.195  amp.  9.  0.151  amp.  10.  1.875  amp. 

11.  0.592  amp.        12.   0.3  ohm. 

Pages  379-380.  1.  349,920  cal.  2.  594,000  cal.  3.  4,356,000 
cal.;  110  volts.  4.  35,700  cal.  in  the  copper,  216,954  cal.  in  the  iron. 

5.  95.12°  C. 

Pages  392-393.  1.  1.89  volts;  2.835  volts;  4.725  volts;  5.67  volts. 
2.  12.2  ohms.  3.  4.5  ohms.  4.  1.222  amp.;  0.846  amp.;  2.068 
amp.;  5.32  ohms.  5.  220  ohms;  55  ohms;  110  ohms;  73.3  ohms;  55 
ohms;  44  ohms;  44  ohms.  6.  660;  29.7  cents.  7.  1.44  ohms. 
8.  19.5  ohms;  11  lamps.  9.  2.42  ohms. 

Page  418.  1.  9.5  volts.  2.  37.5  amp.  3.  75  amp.  4.  1800 
r.  p.  m.;  120  alternations  per  sec.  5.  11,000,000.  6.  12,000,000. 

Pages  433^434.  1.  11.25  ohms;  16.25  ohms.  2.  5  ohms;  7.2 
ohms;  2.2  ohms;  9  amp.  3.  2.25  in.  for+carbon;  1.125  in.  for— car- 
bon. 4.  16.5  ohms.  5.  600  volts;  9.6;  62.5  ohms;  4.17  ohms. 

6.  17.7  ohms;  6.6  ohms.         7.   7.33  ohms;  41,250  watts.         8.   0.4 
ohm;  21,555.5  c.  p.        9.  747.5;  455;  10.77  ohms;  6.92  ohms;  61%. 


522 


APPENDIX 


10.  0.364  amp.;  0.545  amp.  11.  5.46  amp.;  6.54  amp.;  1.08  amp. 
12.  110  volts;  0.327  amp.;  336.4  ohms;  518  cal.  13.  128.6  amp. 
14.  0.0025  ohms;  144,000  cal.  15.  53  lamps.  10.  8.453  amp. 

Pages  442-443.  1.  5  in.  2.  62.5  ft.  3.  1.28  see.  4.  8 
min.  18  sec.  5.  35  min.  nearly.  6.  About  1245  days.  7.  1.45 
m.  8.  9.19  m.  9.  256  c.  p.  10.  Incandescent  lamp  is  2.77 
times  as  bright  as  kerosene  lamp. 


1.    19°. 


2.   50°. 


Pages  456^57. 
5.   1.5  in.        6.   2  ft.        7.   3  ft.;  9  in. 

Page  473.          1.   4.5  in.  2.   9  in. 

5.   4.8  in.;  1:4.        6.   60cm. 


3.    12ft. 


3.   3.2  in. 


4.    Y2'm 


4.   0.2  in. 


TABLE  OF  CONVERSION  FACTORS 


To  CHANGE 

To 

MULTIPLY  BY 

Inches      .        .        ... 

Centimeters         ,       . 

2.54 

Feet         . 

Meters  .        .        »  '"    . 

0.3048 

Miles        . 

Kilometers    .    •».  : 

1.60935 

Meters      .        .     ... 

Inches    .        .        .        . 

39.37 

Meters      .     •  .   ,.  '. 

Feet       ...       .       . 

3.28083 

Kilometers       . 

Miles     .       .       .       . 

0.62137 

Square  inches 

Square  centimeters 

6.4516 

Square  feet      .        .    .   ... 

Square  meters      .        . 

0.0929 

Square  yards  .        .        . 

Square  meters      .        . 

0.8361 

Square  centimeters 

Square  inches 

0155 

Square  meters         ... 

Square  yards 

1.196 

Cubic  inches    . 

Cubic  centimeters 

16.3872 

Cubic  yards     . 

Cubic  meters 

0.7646 

Cubic  centimeters  . 

Cubic  inches 

0.06102 

Cubic  meters  . 

Cubic  yards 

1.308 

Fluid  ounces    . 

Cubic  centimeters 

29574 

§uarts 

Liters     .        .        .  _    v. 

0.9464 

ubic  centimeters  . 

Fluid  ounces         .  '      . 

0.0344 

Liters        .... 

Quarts   .    -..••• 

1.0567 

Grains      .... 

Milligrams    . 

64.7989 

Ounces  (Avoirdupois)    . 

Grams    .... 

28.3495 

Pounds  (Avoirdupois)    . 

Kilograms     . 

0.4536 

Ounces  (Apothecary)     . 

Grams    .        ... 

31.1035 

Pounds  (Apothecary)     . 

Kilograms 

0.3732 

Grams      .... 

Grains    .... 

15.4324 

Kilograms 

Pounds  .... 

2.2046 

Kilowatts 

Horse  Power         .        .  . 

1.34 

Horse  Power  . 

Kilowatts 

0.746 

B.  T.  U.  . 

Calories 

252 

Calories    . 

B.  T.  U. 

0.3968 

APPENDIX 


523 


(For  page  63; 

The  fact  that  the  acceleration  given 

•y2 

by  Fc   is   —  can  be  obtained  from  a 
r 

consideration  of  Fig.  557.  Suppose  a 
body  of  mass  Mto  be  moving  around 
the  circle  whose  center  is  0,  with  a 
uniform  velocity  v.  The  space  AB, 
over  which  it  passes  in  the  time  £,  is 
S  =  vt.  (Formula  2,  page  37.)  Let 
the  time  t  be  taken  as  a  very  short 
time  —  so  short  that  the  arc  AB  is 
practically  equal  to  the  chord  AB.  On 
AB  as  a  diagonal,  complete  the  rec- 
tangle ADBC.  The  distance  the  body 
is  drawn  away  from  A G  toward  0,  by  the  constant  centripetal  force,  is 
practically  equal  to 

CB  =  AD  —  \  at'2.     (Formula  4.) 
Now,  by  geometry,*    AB2  =  AD   x    AE, 


or 
Hence 


v'2t2  —  \  at*  x  2  r. 


=  ar,  and  a  =  — 
r 


(For  page  462) 


FIG.  558 


Fig.  481  shows  how  the 
direction  of  a  ray,  leaving 
water,  may  be  traced  into 
air. 

When  the  angle  of  in- 
cidence NPB,  Fig.  558,  is 
the  critical  angle,  the  angle 
of  refraction,  FBC,  must 
equal  90°.  This  will  be  true 
when  NB  multiplied  by 
four  thirds,  the  index  of 
refraction,  equals  the  radius 
PB  or  BC. 

From  the  similar  triangles 
NPB  and  FEE,  NB  =  FE. 


*  AE  is  the  hypotenuse  of  the  right-angled  triangle  ABE,  and  BD  is  a 
perpend:  cular  dropped  upon  it  from  the  vertex  of  the  right  angle. 


524  APPENDIX 

BD  also  equals  FE.  Hence  BD  =  Nil,  and  since  BC  =  f  of  BD,  it 
also  equals  f  of  NB ;  that  is,  four  thirds  of  NB  equals  the  radius,  and 
the  angle  NPB  is  the  critical  angle. 

The  mathematical  term  for  NB,  when  the  radius  PB  equals  unity,  is 
the  sine  of  the  angle  NPB ;  hence  the  critical  angle  is  that  angle,  the 
sine  of  which  multiplied  by  the  index  of  refraction  equals  unity,  or  the 
sine  of  90°. 

FORMULAS 

PAGE  SUBJECT  FORMULA  NUMBER 

19    Elasticity  e  = Stress  1 

Strain 

37  Motion  (average  speed  or  velocity)     S  =  vt  2 

38  Accelerated  Motion  v  =  at  3 
38                                                        JS  =  \  at*  4 

38  v  =  \/2aS  5 

39  a  =  £a(2«-l)  6 
Falling  Bodies : 

43         From  position  of  rest  v  =  gt  7 

43  s  =  i  0(2  t  -  1)  8 

9 
10 
11 
12 
13 
14 
15 

16 
17 

18 

19 
20 

21 
22 

23 
33,000  x  No.  minutes 


43 

8=%  gt'2 

44 

With  initial  velocity 

v=V+gt 

44 

s=  V+%g(2t  —  1) 

44 

8=  Vt  +  ^gt'2 

47 

Momentum 

b  =  Mv 

47 

Force  in  Absolute  Units 

F=  Ma 

48 

W  =  Mg,  or  M  =  — 

g 

49 

Force  in  Gravity  Units 

F—  JE^ 

g 

63 

Centrifugal  Force 

Fe  =  M^- 

r 

63 

W* 

gr 

71 

Energy 

P.E.  =  Wh 

71 

K.E.  =  \  Mv* 

72 

. 

K.E.  =Ip!! 

74 

Work 

Work  =  FS 

77 

Horse  Power                 Nc 

HP-        No'  foot  P°unds 

APPENDIX 


525 


PAGE              SUBJECT 

FORMULA                                     NUMBER 

80    Mutual  Attraction 

p,       Mm 

Q~   & 

24 

82     Weight  above  Surface  of 

Earth 

W:w  =  d?:&* 

25 

91    Simple  Bendulum 

1*4*^1 

26 

92 

t  :  t'  -  V7:  VF 

27 

97     Efficiency 

E^^w 

28 

97     General  Law  of  Machines 

Pd  =  ED 

29 

100     Lever 

P  :  E  =  E.  arm  :  P.  arm 

30 

103     Wheel  and  Axle  (power 

applied  to  wheel) 

P:  W=r:E 

31 

105    Fixed  Pulley 

P=  W 

32 

105     Movable  Pulley 

P=%W 

33 

106     System  of  Pulleys 

P  =  — 

34 

n 

Inclined  Plane  : 

108        Power  parallel  to  L 

P:  W  =  H:L 

35 

110     Screw 

P:  W  =  p  :  2  irE 

36 

111     Coefficient  of  Friction 

'=1 

37 

135     Liquid  Pressure 

P=  HaW 

38 

149     Specific  Gravity  of  Solids 

SP    T    -           W 

39 

op.  gi.  —                      f 

178     Boyle's  Law 

PV=  P'V 

40 

199     Velocity  of  Sound  in  Air 

v  =  332.4  VI  -f  0.003665  t 

41 

199     Velocity  of  Sound  in  Any  Medium 

i  — 

*=\J 

42 

205     Velocity  and  Wave  Length 

v  =  NL 

43 

206     Velocity  from  Resonance  Tube        v  =  4  N(l  +  0.4  <Z) 

44 

242     Thermometer  Readings 

C  =  f  (F  -  32°) 

45 

242 

F  =  £  C  -f  32° 

46 

242 

C       F-32 

47 

100         180 

^11 

260    Linear  Expansion 

L'  =  L(\  +  Kf) 

48 

265     Laws  of  Boyle  and  Charles 

PV     P'V 

4G 

T           T' 

282     Specific  Heat 

Mts  =  M't's 

50 

526  APPENDIX 

PAGK  SIIIUKOT  FORMULA  NUMBER 

321     Electrical  Attraction  or  Repulsion    /=  ±  QH  51 

327     Electrical  Capacity                               <7  =  ^  52 

3.">5     Resistance  of  Wire                              R  —  K—  53 

d2 

357     Ohm's  Law                                             /=  —  54 

Currents  sent  from  Generators  : 

368         In  series  coupling                              /  = ®E  55 

>S'6  +  R 

359         In  parallel  coupling  /  =  .        56 

359         In  series  and  parallel                        /—  57 

363     Heating  Effects  of  Current                H  =  0.24  I*Rt  58 
390     Combined  Resistance  of  Parallel 

Circuits                                              R  =    9s  59 


414     E.M.F.  of  Dynamo  Jff=5H5L  60 

108 

441     Light  Intensity  L  =  S— *  61 

454,  470     Concave  Mirrors,  Convex 

Lenses  V  _  _L  4.  _  62 

F      Do      Dt 

DEFINITIONS 

Absolute  Zero  :  a  temperature  that  is  273°  Centigrade  below  the  Centi- 
grade zero,  i.e.,  —  273°  C. 

Acceleration :  the  increase  per  second  in  the  speed  of  a  moving  body  for 
each  second  of  its  movement. 

Achromatic  Lens  :  a  lens  that  forms  an  image  of  an  object  without  colored 
edges. 

Actinic  Rays  :  spectrum  wave  lengths  shorter  than  the 'violet. 

Adhesion  :   molecular  attraction  between  molecules  of  different  kinds. 

Agonic  Line  :  a  line  drawn  through  all  places  at  which  the  needle  points 
true  north. 


DEFTNTTrONS  527 

Ammeter :   an  instrument  for  measuring  an  electric  current  in  amperes. 
Amplitude:   the  greatest  distance  that  a  vibrating  body  goes  from  its 

position  of  rest. 

Aneroid  Barometer :   a  form  of  barometer  in  which  no  liquid  is  used. 
Anode :   the  electrode  by  which  the  current  enters  an  electrolyte  in  the 

electrolysis  of  metals. 
Athermanous :   without  heat. 
Atom  :  the  smallest  particle  of  an  element  which  can  either  exist  alone  or 

enter  into  the  composition  of  molecules. 

Barometer :    an  instrument  for  measuring  the  pressure  of  the  atmosphere. 

Beats :  rhythmical  variations  in  the  intensity  of  sound,  alternately  strong 
and  weak. 

Boiling  Point :  the  temperature  at  which  a  liquid  passes  into  the  air  in 
molecular  form,  under  atmospheric  pressure. 

British  Thermal  Unit :  the  amount  of  heat  required  to  raise  the  temper- 
ature of  one  pound  of  water  1°  F. 

Buoyancy :   the  lifting  power  of  a  liquid  upon  a  body  submerged  in  it. 

Calorie :  the  amount  of  heat  required  to  raise  the  temperature  of  one 

gram  of  water  one  degree  Centigrade. 
Calorimetry  :   the  measurement  of  heat. 

Capillary  Attraction:  the  attraction  that  causes  a  liquid  to  rise  in  a  tube. 
Cathode  :   the  electrode  by  which  the  current  leaves  an  electrolyte. 
Centigrade  Scale :    a  temperature  scale  which  makes  the  freezing  point 

of  water  0°  and  its  boiling  point  100°. 
Centrifugal  Force :  the  force  that  causes  the  parts  of  a  rotating  body 

to  tend  to  fly  from  the  center. 
Centripetal  Force  :     the  force  that  prevents  the  parts  of  a  rotating  body 

from  flying  from  the  center. 
Chord  in  Music  :  tones  that  harmonize. 

Chromatic  Scale  :   a  scale  formed  of  the  thirteen  semitones  in  an  octave. 
Cohesion  :  the  attraction  between  particles  of  the  same  kind  at  molecular 

distances. 
Commutator:  a  device  that  changes  the  direction  of  every  other  half 

wave  of  an  alternating  current,  thus  producing  a  direct  current. 
Convection :   the  rising  of  heated  air  or  liquid  setting  up  a  convection 

current. 
Critical  Temperature  :  the  temperature  above  which  no  pressure  however 

great  can  reduce  a  gas  to  a  liquid. 
Crystallization :   the  formation  of  crystals  on  passing  from  a  liquid  to  a 

solid  state. 


528  APPENDIX 

Declination :  the  angle  between  the  direction  the  magnetic  needle  points 
and  the  true  north  arid  south  direction. 

Density :  the  quantity  of  matter  in  unit  volume. 

Dew  Point :  the  temperature  at  which  moisture  in  the  atmosphere  con- 
denses to  liquid  water. 

Diffraction :  the  bending  of  a  ray  of  light  on  passing  the  thin  edge  of  an 
opaque  body. 

Dip :   the  departure  of  a  magnetic  needle  from  a  horizontal  position. 

Ductility  :   the  property  by  which  a  body  can  be  drawn  out  into  a  thread. 

Dyne :  the  absolute  unit  of  force  that  acting  upon  one  gram  of  mass  will 
give  it  an  acceleration  of  one  centimeter  per  second  per  second. 

Efficiency  :   the  ratio  of  output  to  input  in  a  machine. 

Elasticity :   the  property  which  enables  a  body  to  regain  its  original  size 

and  form  after  being  elongated,  compressed,  bent,  or  twisted. 
Electrolyte :  a  compound  subject  to  decomposition  by  an  electric  current; 

in  solution  it  conducts  the  current  from  one  electrode  to  another. 
Electrons  :  particles  smaller  than  the  atom. 

Electroscope  :   an  instrument  for  determining  the  electric  charge  of  bodies. 
Energy  :   the  power  of  doing  work. 
Equilibrant :   a  force  opposite  in  direction  and  equal  in  amount  to  the 

resultant  of  two  or  more  forces. 

Erg :  the  work  done  by  a  force  of  one  dyne  moving  one  centimeter. 
Evaporation :  the  passing  of  a  liquid  into  the  air  by  the  escape  of  its 

molecules,  chiefly  on  account  of  a  rise  in  the  temperature  of  the  liquid. 

Fahrenheit  Scale :   the  temperature  scale  in  which  the  freezing  point  of 

water  is  32°  and  its  boiling  point  212°. 

Focus :   the  point  to  which  rays  of  light,  heat,  etc.,  converge. 
Foot  Pound :   the  gravity  unit  of  work.     The  work  done  in  raising  one 

pound  vertically  against  the  force  of  gravity. 
Force  :   that  which  tends  to  produce,  to  change,  or  to  destroy  the  motion 

of  a  body. 

Fraunhofer  Lines :   Dark  absorption  lines  in  the  solar  spectrum. 
Freezing  Point :   the  temperature  at  which  a  liquid  solidifies. 
Friction :   the  resistance  that  is  encountered  in  moving  (or  trying  to 

move)  one  body  over  another  under  pressure 

Galvanometer:    an  instrument  that  shows  the  electric  current  passing 

through  it  by  the  deflection  of  its  needle. 
Gram  :   the  weight  of  one  cubic  centimeter  of  pure  water  at  4°  Centigrade. 

The  physical  unit  in  the  C.  G.  S.  system. 


DEFINITIONS  529 

Graph :  a  curve  showing  the  continuous  relation  between  two  series  of 

physical  changes. 
Grids :  the  plate  electrodes  of  a  storage  cell. 

Hardness :  resistance  to  wear  by  friction. 

Horse  Power :   a  rate  of  work  of  33,000  foot  pounds  per  minute. 

Humidity :   the  condition  of  the  air  with  respect  to  the  amount  of  moisture 

in  it. 
Hydrometer :  a  floating  instrument  for  determining  the  specific  gravities 

of  liquids. 

Impenetrability :   a  property  of  matter  that  prevents  two  bodies  occupying 
the  same  space  at  the  same  time. 

Incidence,  Angle  of:  the  angle  between  a  ray  of  light  and  the  perpendicu- 
lar to  the  surface  on  which  it  strikes. 

Inertia :  the  tendency  of  a  body  to  retain  its  condition  of  rest  or  motion. 

Insulator :   a  substance  that  does  not  carry  a  current  of  electricity. 

Interference :  when  the  trough  of  one  series  of  waves  meets  the  crest  of 
another  series. 

Isochronous :  uniform  in  time ;  vibrations  made  in  the  same  time  are 
isochronous. 

Joule :  a  unit  of  work  equal  to  10,000,000  ergs. 

Kilogram :   1000  grams. 

Kinetic  Energy :  the  energy  of  motion. 

Lactometer  :   a  form  of  hydrometer  used  for  testing  milk. 
Liter :   a  unjt  of  liquid  capacity,  a  cubic  decimeter. 
Lycopodium  Powder :  the  spores  from  a  certain  class  of  plants. 

Machine  :  a  mechanical  device  for  applying  force  advantageously. 
Magnetic  Field :   a  space  occupied  by  magnetic  lines  of  force. 
Malleability :  the  property  that  allows  a  body  to  be  rolled  or  beaten  into 

thin  sheets. 

Manometer :   a  device  for  measuring  gas  pressure. 
Maxwell :   a  line  of  magnetic  force. 
Meter :  the  ten  millionth  part  of  the  quadrant  of  the  earth.     The  C.  G.  S. 

unit  of  length. 

Mil :   the  thousandth  part  of  an  inch. 

Molecule  :  the  smallest  division  of  matter  that  retains  its  identity. 
Moment  of  a  Force  :  the  product  of  the  force  by  its  lever  arm. 

Node :  the  place  of  no  vibration  in  a  cord  producing  static  waves. 
Rev. 


530  APPENDIX 

Octave :  the  eighth  tone  of  a  scale  having  double  the  nuniber  of  vibra- 
tions of  its  fundamental. 
Osmose  :   the  passage  of  a  liquid  through  a  porous  membrane. 

Plane  Mirror :   a  plane  totally  reflecting  surface. 

Plane  Polarized  Light :   light  formed  by  vibrations  that  are  parallel  to 

each  other. 

Plumb  Line :   a  vertical  line. 

Polariscope  :   a  device  for  the  study  of  substances  by  polarized  light. 
Porosity:   a  property  possessed  by  a  body  in  which  the  particles  that 

compose  it  do  not  fill  its  entire  volume. 

Relay  :   a  high  resistance  electromagnet  in  series  with  the  main  line  in  a 

telegraphic  system. 
Resistance :  that  which  opposes  the  passage  of  an  electric  current  through 

a  conductor. 
Rheostat :   a  resistance  box  for  commercial  use. 

Semitone  :  the  interval  between  a  tone  and  its  sharp. 

Specific  Gravity :  the  relative  weight  of  a  body  compared  with  the  weight 
of  an  equal  volume  of  water. 

Specific  Heat :  the  number  of  calories  required  to  change  the  temperature 
of  one  gram  of  a  substance  one  degree  Centigrade. 

Spectrum  :  the  group  of  wave  lengths  into  which  a  beam  of  light  is  sepa- 
rated by  a  prism  or  by  a  diffraction  grating. 

Strain :  the  change  of  shape  or  size  produced  when  a  body  is  under  a 
stress. 

Stress :  a  force  bearing  upon  a  body  and  tending  to  change  its  size  or 
shape. 

Tenacity :   the  resistance  of  a  body  to  being  pulled  apart. 
Thermostat :   a  device  for  announcing  when  the  temperature  of  a  room  is 
too  hot  or  too  cold. 

Vacuum  :  a  space  exhausted  of  air  or  gas. 

Vapor :  gaseous  matter,  of  a  substance  that  is  liquid  at  normal  tempera- 
ture and  pressure. 

Volt :  that  .electrical  pressure  that  will  send  one  ampere  of  current 
through  one  ohm  of  resistance. 

Watt :   one  Joule  of  power  per  second.     T^  of  a  horse  power. 


SUPPLEMENTARY  QUESTIONS  AND  PROBLEMS 

I.  States  and  Properties  of  Matter. 

1.  Define  a  solid,  a  liquid,  a  gas.    Explain  the  kinetic  theory  of 
matter  as  applied  to  each. 

2.  State  the  difference  between  general  and  specific  properties  of 
matter.     Name  and  define  several  general  and  several  specific  properties. 

3.  Define  and  give  an  example  of  mass,  weight,  force.     Name  the 
unit  of  each. 

4.  Write  the  value  of  /x  (one  micron)  in  millimeters. 

II.  Motion,  Velocity,  and  Force. 

1.  On  December  12,  1920,  Lecointe,  a  French  aviator,  broke  the  air- 
plane speed  record  by  flying  4  kilometers  in  46  seconds.     What  was  his 
speed  in  feet  per  second,  in  miles  per  hour,  in  kilometers  per  hour  ? 

2.  An  airplane  one  mile  high  traveling  at  the  rate  of  90  mi.  per  hr. 
drops  a  bomb  when  directly  over  the  high   school.     How  far  from  the 
building  would  the  projectile  strike  the  ground  if  its  course  were  not  affected 
by  the  resistance  of  the  air  ? 

3.  A  photograph  of  a  luminous  bomb  dropped  from  a  horizontally 
moving  airplane  was  made  at  night  and  the  path  differed  slightly  from  the 
path  shown  in  Fig.  15.     Mention  two  possible  reasons  for  the  difference. 

4.  A  boat  is  rowed  across  a  river  heading  in  a  direction  at  a  right 
angle  to  the  current  with  twice  its  speed,  landing  on  the  opposite  bank  1.5 
miles  downstream  from  the  starting  point.     Find  the  width  of  the  river 
and  the  distance  the  boat  traveled.     Make  a  diagram  of  its  path  to  scale. 

5.  Two  boys  fasten  ropes  to  the  bag  on  second  base  of  a  baseball 
diamond.     One  pulls  toward  the  first  base  and  the  other  toward  the  third 
base,  each  pull  being  25  Ib.     What  must  be  the  amount  and  direction  of  a 
pull  that  will  hold  the  bag  in  place?     Make  a  diagram  to  scale. 

6.  An  airplane  whose  speed  is  85  mi.  per  hr.  in  still  air  drives  into  a 
head  wind  that  retards  it  25  mi.  per  hr.     It  then  turns  and  goes  with  the 
wind.    Then  it  heads  in  a  direction  at  a  right  angle  to  the  wind.    Find 
the  velocity  of  the  plane  in  each  case.     Make  a  diagram  for  each  to  scale. 

7.  Give  the  relative  tendency  of  an  automobile  to  skid  at  velocities  of 
20  and  30  mi.  per  hr.  as  compared  with  a  velocity  of  10  mi.  per  hr. 

531 


532  APPENDIX 

in.   Energy  and  Work. 

1.  A  3-lb.  projectile  has  a  velocity  of  2000  ft.  per  sec.     What  kind 
of  energy  has  it  ?     How  much  ?     What  would  be  the  effect  of  doubling 
its  velocity  ?  of  doubling  its  weight  ? 

2.  If  we  make  no  allowance  for  the  resistance  of  the  air,  how  high 
would  the  projectile  of  problem  1  go  if  fired  vertically  upward  with  the 
same  velocity  ?     What  would  be  its  potential  energy  at  the  top  of  its 
path  ?     What  would  be  its  kinetic  energy  on  striking  the  ground  ?     What 
would  be  its  velocity  on  striking  the  ground  ? 

3.  It  requires  a  force  of  396  Ib.  to  move  an  automobile  over  a  level 
road.     How  much  work  will  be  done  in  moving  it  5000  ft.  ?     What  horse 
power  will  be  required  to  do  it  in  3  minutes  ? 

4.  A  constant  pull  of  470  Ib.  is  required  to  move  a  loaded  truck  at  the 
rate  of  20  mi.  per  hr.     What  horse  power  does  the  motor  develop  ? 

IV.  Machines. 

1.  What  is  meant  by  the  efficiency  of  a  machine  ?     Why  is  it  always 
less  than  100%  ?    Explain  this  with  reference  to  some  especial  machine. 

2.  A  down  pull  of  25  Ib.  applied  10  ft.  from  a  fulcrum  balances  a 
weight  of  150  Ib.     How  far  from  the  fulcrum  is  the  weight  placed  ? 
What  class  of  lever  is  it  ? 

3.  A  weight  of  750  Ib.  placed  1.5  ft.  from  a  fulcrum  is  balanced  by  a 
lift  at  the  end  of  a  lever  arm  12.5  ft.  long.     What  is  the  amount  of  the  lift  ? 
What  class  of  lever  is  it  ? 

4.  A  crank  18  in.  long  is  used  to  turn  an  axle  5  in.  in  diameter.     A 
rope  1  in.  in  diameter  is  wound  around  this  axle  and  a  bucket  holding  a 
cubic  foot  of  water  is  attached  to  this  rope  and  is  raised  from  a  well. 
What  force  must  be  applied  to  the  handle  to  balance  the  weight  of  the  water? 

5.  Find  the    coefficient  of  friction  between  a  sled  runner  and  snow 
when  it  takes  a  pull  of  24  Ib.  to  draw  a  boy  and  sled  weighing  136  Ib. 

V.  Liquids. 

1.  A  cubical  block  of  wood  is  loaded  so  that  it  will  sink  in  water  with 
its  top  in  the  surface  of  the  water.     What  keeps  it  from  sinking  ?     Why 
does  it  not  move  to  one  side  ? 

2.  How  much  water  will  a  block  of  pine  wood  displace  ?     How  much 
will  a  block  of  marble  displace  ? 

3.  What  is  the  density  in  grams  per  c.c.  of  a  body  the  specific  gravity 
of  which  is  2.57  ?     What  is  its  density  in  pounds  per  cu.  ft.  ? 

4.  An  empty  bottle  weighs  64.7  grams.     The  weight  of  the  bottle  full 
of  water  is  278.5  grams.     The  weight  of  the  bottle  full  of  alcohol  is  239.8 
grams.     Find  the  specific  gravity  of  the  alcohol. 


SUPPLEMENTARY    QUESTIONS  533 

VI.    Gases. 

1.  How  does  the  motion  of  the  molecules  in  a  gas  differ  from  that  in 
a  liquid  or  a  solid  ? 

2.  What  determines  the  buoyant  or  lifting  force  of  the  atmosphere  on 
a  balloon?    Is  there  any  limit  to  the  height  to  which  a  balloon  will  rise? 
Why? 

3.  Why  is  mercury  used  in  making  a  barometer  ? 

4.  To  what  height  will  a  suction  pump  draw  water?    To  what  height 
will  a  force  pump  force  it  ? 

VH.    Sound. 

1     Give  examples  to  show  that  sound  is  transmitted  through  solids, 
liquids,  gases. 

2.  Under  what  conditions  will  a  vibrating  body  produce  a  musical 
tone  ?    What  is  the  difference  between  a  musical  tone  and  a  noise  ? 

3.  Why  is  the  tone  of  an  open  pipe  an  octave  lower  than  the  tone 
produced  by  the  same  pipe  when  the  end  is  closed  ? 

VIH.   Heat. 

1.  What  different  properties  of  mercury  are  used  in  the  operation  of  a 
thermometer  and  of  a  barometer  ? 

2.  Explain  the  difference  between  holding  a  burning  match  in  the 
fingers  and  holding  the  end  of  a  short  piece  of  copper  wire  when  the  other 
end  is  in  a  gas  flame. 

3.  Will  heat  from  a  source   of  high  temperature  pass  through  a 
vacuum  ?    Give  an  example. 

4.  Give  two  reasons  why  a  bicycle  pump  becomes  hot  when  pumping 
up  a  tire. 

5.  A  gas  stove  has  two  burners,  burner  A  using  much  more  gas  than 
burner  B.     Over  which  of  these  would  you  place  a  teakettle  to  heat  it  to 
the  boiling  point  ?    Why  ?    Over  which  would  you  place  it  to  keep  it 
boiling  ?     Why  ? 

6.  Explain  why  the  uncovered  pipes  of  an  ammonia  ice  machine  are 
covered  with  ice. 

7.  Why  is  dew  formed  on  grass  ?    Why  is  frost  formed  ?    Explain 
the  difference. 

8.  Give  an  example  of  the  transformation  of  mechanical  energy  into 
heat.     Give  an  example  of  the  reverse. 

IX.   Electricity. 

1.    How  could  you  determine  the  kind  of  electrification  of  charged 
bodies  by  the  use  of  a  positively  charged  pith  ball  ? 


534  APPENDIX 

2.  How  can  a  body  be  charged  by  induction  ? 

3.  How  does  a  lightning  rod  tend  to  prevent  the  destruction  of  build- 
ings by  lightning  ? 

4.  Find  the  resistance  of  1000  ft.  of  copper  wire  having  a  diameter  of 
0.0201  in.,  the  value  of  K being  10.38. 

5.  Write  Ohm's  law  in  three  ways,  each  in  the  form  of  a  sentence. 

6.  Six  cells  are  coupled  in  series  with  an  external  resistance  of  12 
ohms.     What  current  will  they  send  if  each  cell  has  an  E.  M.  F.  of  1.5 
volts  and  an  internal  resistance  of  0.4  ohms  ? 

7.  What  current  will  a  battery  of  4  dry  cells  coupled  in  parallel  send 
through  100  ft.  of  No.  18  copper  wire,  the  E.  M.  F.  of  each  cell  being 
1.5  volts  and  its  internal  resistance  0.6  ohms  ? 

8.  In  what  direction  would  you  send  the  current  around  an  electro- 
magnet in  order  to  make  the  end  that  faces  you  the  north  pole  ? 

9.  Make  a  diagram,  showing  how  a  single  bell  may  be  rung  by  each 
of  two  push  buttons. 

10.  Make  a  diagram  showing  how  a  single  push  button  may  ring  two 
bells  at  the  same  time. 

11.  Two  parallel  circuits  of  3  and  5  ohms  respectively  are  coupled  to 
two  binding  posts  having  a  potential  difference  of  20  volts  between  them. 
What  is  the  parallel  resistance  of  the  two  circuits  ?     What  is  the  current 
in  each  branch  ?     What  is  the  total  current  ? 

12.  A  60-watt  Mazda  lamp  is  run  on  a  110-volt  circuit.    What  current 
does  it  take  ?    What  is  its  resistance  ? 

i  X.   Light. 

1.  How  do  we  see  a  luminous  body  ?    How  do  we  see  a  non-luminous 
body? 

2.  A  man  is  reading  at  a  certain  distance  from  an  incandescent  lamp 
and  finds  the  light  too  poor.     He  turns  on  another  similar  lamp  from  the 
same  bracket.     How  much  is  the  illumination  increased  ?     How  much 
would  it  have  been  increased  if  he  had  moved  halfway  to  the  lamp  in- 
stead of  turning  on  the  second  lamp  ? 

3.  A  certain  projecting  lamp  makes  a  picture  too  large  for  the  screen. 
What  kind  of  a  lens  would  you  combine  with  the  projecting  lens  of  the 
lantern  to  reduce  the  size  ?    Why  ? 

4.  What  is  the  advantage  of  using  a  frosted  bulb  lamp  instead  of  a 
clear  glass  bulb  ? 

5.  What  is  the  advantage  of  putting  a  white  glass  globe  on  a  lamp 
bulb? 


INDEX 


Aberration,  455,  471,  474. 
Absolute  temperature,  265. 
Absolute  unit  of  force,  47. 
Absolute  units  of  work,  74. 
Absolute  zero,  264. 
Absorption  of  gases,  184. 

of  heat,  257. 

of  liquids,  125. 
Accelerated  motion,  36. 
Acceleration,  36,  37. 

negative,  46. 
Accumulator  cell,  378. 
Achromatic  lens.  475. 
Actinic  rays,  485. 
Adhesion,  21,  123. 
Agonic  line,  310. 
Air,  composition  of,  166. 

compressed,  158-163. 

effects  of  expansion  in,  266. 

height  of,  176. 

liquefied,  266,  276. 

pressure  of,  158-168. 

resistance  of,  39. 

sound  transmitted  by,  195-199. 

water  vapor  in,  269-273. 

wave  motion  in,  196. 

weight  of,  165. 

Air  columns,  vibration  of,  224. 
Air  pump,  159. 
Air  thermometer,  243. 
Airplane,  168,  171. 

instruments  used  in,  170. 
Alcoholmeter,  154. 
Algebraic  balance,  101 . 
Alternating  current,  409. 
Alternator,  410. 
Ammeter,  380,  383. 
Ammonia,  277. 
Ampere,  354. 
Amplitude  of  oscillation  or  vibration, 

90,  192,  211. 
Aneroid  barometer,  173. 


Angle,  critical,  460. 

of  deviation,  465. 

of  elevation,  46. 

of  incidence,  62,  444,  457. 

of  reflection,  62,  444. 

of  refraction,  457. 
Anion,  374. 
Annealing,  25. 
Anode,  374. 

Anomalous  expansion  of  water,  262. 
Aperture  of  mirror,  449. 
Arc  lamp,  420. 

Archimedes,  Principle  of,  146. 
Arm  of  lever,  100. 
Armature,  of  magnet,  368. 

of  dynamo,  405. 
Athermanous  substance,  258. 
Atmosphere,  166;  see  Air. 

unit  of  pressure,  172. 
Atmospheric  electricity,  342. 
Atom,  10,  518. 
Attraction,  law  of,  80. 
Audibility,  limit  of,  235. 
Audion,  509-510. 
Aurora  Borealis,  344. 
Automobile,  85,  296-298,  378. 
Axis,  of  lens,  466. 

of  mirror,  449. 

of  suspension  of  pendulum,  93. 

Back  electromotive  force,  414. 
Balance,  102. 

Balancing  columns,  method  of,  153. 
Balloon  ascensions,  177. 
Barograph,  174. 
Barometer,  172. 
Battery,  347,  358;  see  Cells. 
Beam  of  light,  436. 
Beats,  209. 
Becquerel  rayb,  516. 
Bell,  electric,  369;  nodes  and  loops 
in,  224. 


535 


536 


INDEX 


Bichromate  cell,  351. 
Block  and  tackle,  106. 
Bodies,  defined,  10. 
Boiling,  273. 
Boiling  point,  240. 
Bole,  47. 

Boyle's  Law,  177,  265. 
Breaking  weight,  22. 
Brennan  Monorail  car,  66. 
Brush  discharge,  340. 
B.  T.  U.,  281. 
Bunsen  photometer,  441. 
Buoyancy,  147. 

Cadmium  Standard  cell,  356. 
Calorie,  281. 
Calorimetry,  281-285. 
Camera,  438,  497. 
Camouflage,  481. 
Capacity,  electrical,  327. 

specific  inductive,  330. 
Capacity,  unit  of,  31. 
Capillarity,  124. 
Capillary  attraction,  125. 
Carnegie,  311. 
Cathode,  374. 
Cathode  rays,  511. 
Cation,  374. 
Cells,  galvanic,  347,  349. 

chemical  action  in,  347. 

loss  of  potential  in,  353. 

grouping  of,  358. 

polarization  of,  348. 

resistance  of,  390. 

standard,  356. 

storage,  376. 
Center,  of  curvature,  449,  466. 

of  gravity,  82. 

of  moments,  58. 

of  oscillation,  93. 

of  percussion,  93. 

of  pressure  of  liquids,  135-136. 
Centigrade  scale,  241. 
Centimeter,  30. 
Centrifugal  force,  63,  81. 
Centrifugal  pump,  183. 
Centripetal  force,  63. 
C.  G.  S.  sjfstem,  28. 
Charge,  unit,  321. 
Charles,  Law  of,  265. 
Chemical  action,  source  of  heat,  247. 

source  of  electric  current,  346. 


Chemical  change,  9. 

Chemical  rays,  485. 
Chloride  accumulator  cell,  378. 
Chord,  in  music,  215. 
Chromatic  aberration,  474. 
Chromatic  scale,  217. 
Chromic  acid  cell,  351. 
Circuit,  347,  426. 
Clark  cell,  356. 
Clinical  thermometer,  244. 
Closed  circuit,  347. 
Coefficient,  of  cubical  expansion,  262. 
of  friction,  111. 
of  linear  expansion,  260. 
Coherer,  in  wireless  telegraph  system, 

507. 

Cohesion,  21,  119. 
Collimator,  481. 

Collision,  heat  produced  by,  247. 
Color,  473. 

Comma,  in  music,  216. 
Communicating   vessels,    liquids   in, 

139. 

Commutator,  404. 
Compass,  302. 
Complementary  colors,  480. 
Components,  53. 
Composition,  of  forces,  52. 

of  velocities,  61. 
Compound  dynamo,  409. 
Compressed  air,  uses  of,  162. 
Compressibility,  16,  158. 
Compression,  heat  produced  by,  247. 
Concave  lenses,  465,  469. 
Concave  mirrors,  449. 
Condensation,  in  sound,  196. 

of  vapor,  275. 
Condenser,  distillation,  275. 

electrical,  332. 
Condensing  pump,  161. 
Conduction  of  heat,  248. 

onductors,  electrical,  322. 

onjugate  foci,  452. 
Conservation  of  energy,  73. 
Constant  force,  effect  of,  39. 

onvection,  251. 

onverging  lenses,  465. 

onverter,  electrical,  431. 
Convex  lenses,  470. 

onvex  mirror,  454. 

opper  wire  table,  355. 

ouple,  60. 


INDEX 


537 


Critical  angle,  460. 
Critical  temperature,  276. 
Crookes,  Professor  William,  511. 
Crowfoot  cell,  350. 
Crystallization,  25. 
Curie,  Madame,  516. 
Current,  electric,  defined,  346. 

effects  of,  362-379. 

energy  of,  391. 

induced,  393. 

measurement  of,  383. 

parallel  currents,  393. 

production  of,  346-360,  393-415. 

unit  of,  354. 
Curve  or  graph,  45. 
Curvilinear  motion,  34,  62. 
Cycle,  in  dynamo,  409. 
Cyclonic  storm  pressure,  175. 

Dalton,  John,  518. 
Daniell  cell,  349. 
D' Arson val  galvanometer,  381. 
Davy  safety  lamp,  249. 
Declination,  magnetic,  310. 
Deflection  of  needle,  365. 
Degrees  of  temperature,  241. 
Density,  31,  148,  158. 

table  of  densities,  150. 
Detector  galvanometer,  380. 
Deviation,  angle  of,  465. 
Dew-point,  271. 
Diathermanous  substance,  258. 
Diatonic  scale,  214. 
Dielectrics,  323. 
Difference  of  potential,  denned,  326. 

measurement  of,  380,  382. 

unit  of,  353. 
Diffraction,  487. 
Diffusion,  of  gases,  187. 

of  light,  443. 

of  liquids,  126. 
Dip,  magnetic,  309. 
Dipping  needle,  309. 
Dirigible,  8. 

Discharge,  338-341,  402. 
Discord,  219. 
Dispersion  of  light,  473. 
Distillation,  275. 
Divisibility,  1G. 
Doppler's  principle,  213,  485. 
Double  refraction,  489. 
Drum  armature,  406. 


Dry  cell,  352. 
Ductility,  24. 
Dynamics,  34. 
Dynamo,  403,  408. 
Dyne,  47. 

Earth,  magnetism  of,  308. 

Ebullition,  273. 

Echoes,  200. 

Edison,  Thomas  A.,  234,  515. 

Efficiency,  97,  360. 

Effort,  97. 

Einstein,  Albert,  32,  426. 

Elastic  fatigue,  19. 

Elastic  limit,  18. 

Elasticity,  17-21,  158. 

Electric  bell,  369. 

Electric  couple,  415. 

Electric  current,  346;  see  Current. 

Electric  heating,  362. 

Electric  lighting,  420,  503 

Electric  motor,  412,  429. 

Electric  railways,  428. 

Electric  telegraph,  370. 

Electric  washing  machine,  -198. 

Electric  welding,  431-432. 

Electric  whirl,  345. 

Electrical  capacity,  327. 

Electrical  discharge,  effects  of,  333, 

338-341. 

Electrical  energy,  391,  431. 
Electrical  field,  328. 
Electrical  machines,  335. 
Electrical  potential,  326;  see  Differ- 
ence of  potential. 
Electrical  resonance,  506. 
Electricity,  318-484. 

atmospheric,  342-344. 

commercial  applications,  418-431. 

current,  346;  see  Current. 

distribution  over  a  conductor,  324 

frictional,  318,  323. 

positive  and  negative,  320. 

static,  318-345. 

two  kinds  of,  320,  323. 

unit  charge  of,  321. 
Electrification,  318. 
Electrodes,  374. 
Electrolysis,  374. 
Electrolyte,  374. 
Electromagnet,  366. 
Electrometallurgy,  375. 


538 


INDEX 


Electromotive  force,  defined,  348, 352 

measurement  of,  382. 

unit  of,  356. 
Electrons,  10,  517. 
Electrophorus,  331. 
Electroplating,  375. 
Electroscope,  321. 
Electrostatic  induction,  328. 
Electrotyping,  376. 
Emanation,  517. 
E.  M.  F.,  352,  414. 
Energy,  70. 

conservation  of,  73. 

transformation  of,  72. 
Engines,  290-298. 
Equal  temperament,  217. 
Equilibrant,  55. 

Equilibrium,    general    condition    of, 
57,  60. 

in  liquids,  139. 

of  any  number  of  forces,  100. 

of  parallel  forces,  59. 

of  two  forces,  53,  54. 

stable,  unstable,  neutral,  85. 
Erg,  74. 

Escapement,  94. 
Ether,  nature  of  the,  254. 
Evaporation,  270. 
Exciter,  410. 

Expansibility  of  gases,  157. 
Expansion,  by  heat,  259-266. 

anomalous,  262. 

cubical,  261. 

linear,  260. 

Experiment,  defined,  12. 
Eye,  499. 

Fahrenheit  scale,  241. 

Fall  of  potential  along  a  conductor, 

385. 

Falling  bodies,  39-44. 
Field,  electrical,  328. 

magnetic,  308. 
Films,  122. 

Flames,  musical,  sensitive,  233,  234. 
Flaming  arc  lamp,  422. 
Flat,  in  music,  217. 
Fleuss  pump,  160. 
Floating  bodies,  148. 
Fluid,  defined,  11. 
Fluorescence,  512. 
Fluoroscope,  515. 


Focal  length,  450,  468. 
Foci,  of  lenses,  467. 

of  mirrors,  449-455. 
Focus,  defined,  449. 
Foot,  29. 
Foot  pound,  74. 
Foot  poundal,  74. 
Force,  defined,  47. 

electromotive,  356. 

lines  of,  see  Lines. 

measurement  of,  47. 

moment  of,  57. 
Force  pump,  183. 
Forced  vibrations,  207. 
Forces,  composition  of,  52. 

graphical  representation  of,  52. 

parallel,  58-60,  82,  83. 

resolution  of,  56. 
Formulas,  524. 
Fountain  in  vacuo,  167. 
F.  P.  S.  system,  28. 
Franklin,  Benjamin,  342. 
Fraunhofer  lines.  483. 
Freezing  mixture,  269. 
Freezing  point,  240,  268. 
Friction,  111. 

coefficient  of,  111. 

electricity  produced  by,  318,  323, 
335. 

heat  produced  by,  247. 
Fulcrum,  99. 

Fuse  wires  for  electric  circuits,  363. 
Fusion,  267. 

heat  of,  283. 

g,  determination  of,  94. 
Galileo,  40,  494. 
Galton's  whistle,  235. 
Galvanic  cell,  347. 
Galvanometer,  380. 

and  shunt,  390. 

deflection  of  needle  in,  305. 
Galvanoscope,  380. 
Gas  engines,  294. 
Gas  holder,  163. 
Gas,  illuminating,  163-165,  174. 
Gas  mask,  185. 
Gases,  11,  157-190. 

absorption  of,  184. 

convection  in,  252. 

diffusion  of,  187. 

elastieity  of,  158. 


INDEX 


539 


Gases,  expansibility  of,  157. 

expansion  of,  by  heat,  264. 

heat  conductivity  of,  250. 

pressure  on,  177-180. 

sound  transmitted  by,  195. 

weight  of,  165. 
Gauss,  308. 
Geissler  tubes,  403. 
Goneral  properties,  14. 
Gram,  31. 
Graph,  45. 
Gravitation,  80. 
Gravity,  80. 

acceleration  of,  40. 

center  of,  82. 

specific,  146-156. 
Gravity  cell,  350. 
Gravity  unit,  of  force,  48. 

of  work,  74. 
Grids,  378. 
Gyroscope,  65. 

Hardness,  24. 
Harmonic  motion,  191. 
Harmonics,  in  music,  223. 
Harmony,  219. 
Hartl  optical  disk,  444. 
Hearing,  range  of,  235. 
Heat,  237-299. 

absorption  of,  257. 

and  work,  287-299. 

conductors  of,  248. 

effects  of,  238,  259,  267,  269. 

expansion  caused  by,  238,  259-266. 

kinetic  theory  of,  237. 

luminous,  258. 

measurement  of,  281. 

mechanical  equivalent  of,  287. 

of  fusion,  283. 

radiation  of,  254. 

reflection  of,  256. 

sources  of,  246,  339,  362. 

specific,  281. 

transmission  of,  248. 

of  vaporization,  284. 

wave  length,  485. 
Heating,  electric,  363. 

hot  water,  251. 
Heat  lightning,  343. 
Heat  loss  in  electric  current,  363. 
Heat  of  fusion,  283. 
Heat  of  vaporization,  284. 


Heat  rays,  485. 
Helmholtz  resonators,  232. 
Hertz  waves,  506. 
Hoffman's  apparatus,  374. 
Holtz  machine,  335. 
Homogeneous  substance,  255. 
Hooke's  Law,  18. 
Horse  power,  76. 
Hot  water  heating  system,  251. 
Humidity,  272. 
Hydraulic  press,  130. 
Hydraulic  ram,  139. 
Hydrometer,  153. 
Hydrostatic  press,  130. 
Hygrometer,  272. 
Hypothesis,  13. 

Ice,  266-269. 

manufactured,  277. 
Ice-pail  experiment,  329. 
Illuminating  gas,  163-165,  174. 
Illumination,  intensity  of,  439,  503. 
Image,  defined,  438. 
Images,  formed  by  lenses,  470. 

formed  by  mirrors,  445—449. 

formed  through  an  opening,  438. 

multiple,  447. 

real,  453,  454. 

virtual,  445,  453,  454. 
Impact,  heat  produced  by,  247. 
Impenetrability,  14. 
Incandescent  lighting,  423. 
Incidence,  angle  of,  62,  444,  457. 
Inclination,  magnetic,  309. 
Inclined  plane,  108. 
Inclosed  arc  lamp,  421. 
Indestructibility,  16. 
Index  of  refraction,  459. 
Induced  currents,  328,  393-415. 
Induction,  electrostatic,  328. 

magnetic,  313. 

of  currents,  328,  393-415. 

self-,  399. 

Induction  coil,  400. 
Induction  machines,  335. 
Inertia,  17. 
Initial  velocity,  44. 
Insulators,  322. 
Interference,  in  light,  486. 

in  sound,  203. 

in  wave  motion,  203. 
Internal  resistance,  357,  390. 


540 


INDEX 


International    prototype    standards 

30. 

Intervals  in  music,  215. 
lonization,  517. 
Ions,  374. 
Isochronous,  94. 

Joly  photometer,  441. 

Joule,  76. 

Joule's  equivalent,  288. 

Kelvin,  Lord,  10,  402. 

Keynote,  216. 

Kilogram,  31. 

Kilogramme ter,  74. 

Kilowatt,  77,  Kilowatt-hour,  391. 

Kinetic  energy,  71. 

Kinetic  theory,  11,  157,  237. 

Kinetics,  34. 

Lactometer,  154. 
Lantern,  optical,  495. 
Law,  physical,  13. 
Leclanch6  cell,  351. 
Length,  unit  of,  29. 
Lenses,  465-472,  475. 
Lenz'a  law,  412. 
Lever,  99. 

bent,  101. 

compound,  102. 

law  of  the,  100. 
Leyden  jar,  333,  341,  346. 
Lifting  jack,  110. 
Lifting  magnet,  368. 
Lifting  pump,  182. 
Light,  435-505. 

denned,  435. 

diffused,  443. 

dispersion  of,  473. 

intensity  of,  439. 

interference,  486. 

measurement  of,  440. 

polarized,  488. 

propagation  of',  436. 

reflection  of,  443. 

refraction  of,  457. 

velocity  of,  439. 

waves,  wave  length,  474,  484. 
Lighting,  electric,  420,  503. 
Lightning,  343. 
Lightning  rods,  344. 
Lines  of  magnetic  force,  304. 

action  of,  307,  394. 


Liquids,  11,  119-156. 

absorption  of,  125. 

diffusion  of,  126. 

equilibrium  in,  132. 

expansion  of,  262. 

heat  conductivity  of,  249. 

mechanics  of,  129-145. 

molecular  forces  in,  119-129. 

pressure  of,  129-141. 

sound  transmitted  by,  195,  199. 

spherical  form  of,  119. 

surface  tension,  120. 
Liter,  32. 
Local  action,  348. 
j  Longitudinal  vibrations,  192. 
Loops,  in  a  sounding  body,  222. 
Luminous  arc,  422. 
Luminous  bodies,  435. 
Luminous  heat,  258. 
Lycopodium  powder,  120. 

Machines,  96-118. 
general  law  of,  97. 
simple,  98.  . 

Magnetic  declination,  310. 
Magnetic  drag,  414. 
Magnetic  effects  of  electric  currents 

364-373. 
Magnetic  field,  308. 

of  dynamo,  407. 
Magnetic  induction,  313. 
Magnetic  lines  of  force,  304,  364,  394. 
Magnetic  meridians,  302. 
Magnetic  needle,  302. 
Magnetic  permeability,  306. 
Magnetic  substances,  301. 
Magnetism,  300-317. 

explanation  of,  315. 

of  the  earth,  308. 
Magneto,  404. 
Magnets,  300. 

distribution  of  magnetism  in,  304. 

effect  of  breaking,  316. 

effect  of  heating,  316. 

electro-,  366. 

lifting,  368. 

mutual  action  of,  303. 

poles  of,  302. 
Malleability,  24. 
Manometer,  179,  241, 
Vlanometric  flames,  231. 
Marconi,  Gugljelmo.  507, 


INDEX 


541 


Mariotte,  Edme,  178. 

Mass,  27. 

Matter,  defined,  10. 

kinetic  theory  of,  11. 

properties  of,  14«-33. 

states  of,  10. 

Maximum  current  of  cells,  360. 
Maximum  efficiency,  360. 
Maxwell,  line  of  force,  308,  366. 
Mayer's  floating  magnets,  304. 
Measure  of  electrical  attraction,  320. 
Measurements,  27. 

electrical,  380-392. 
Mechanical  advantage,  98. 
Mechanical  equivalent  of  heat,  287. 
Mechanical  powers,  98. 
Mechanics,  34. 
Melting  points,  267.  • 
Mercury  arc  lamp,  422. 
Mercury  thermometer,  239-242. 
Metallic  thermometer,  243. 
Metallized  filaments,  425. 
Meter,  28. 
Metric  system,  28. 
Microscope,  491. 
Mil,  355. 
Millimeter,  29. 
Millivoltmeter,  383. 
Mirrors,  concave,  449. 

convex,  454. 

plane,  445. 

revolving,  231. 
Molecular  magnets,  315. 
Molecules,  10. 
Moment  of  a  force,  57. 
Momentum,  47. 
Monochord,  221. 
Morse  alphabet,  373. 
Motion,  kinds  of,  34,  36,  57,  62,  191. 

laws  of,  49-51. 

reciprocating,  291. 

reflected,  62. 

simple  harmonic,  191. 
Motor,  electric,  412,  429. 
Mouthpieces    of    wind    instruments, 

224. 

Multiple  grouping  of  cells,  358. 
Music,  210. 
Musical  flames,  233. 
Musical  instruments,  217,  223,  224. 
Musical  scale,  214. 
Myriawatt,  77. 


Negative  electricity,  320. 

Newton's  disk,  479. 

Newton's  law  of  motion,  49-51. 

Newton's  rings,  486. 

Nicol's  prism,  489. 

Nodes,  222. 

Noise,  210. 

Normal,  444. 

North  pole,  magnetic,  302,  308. 

Northern  Lights,  344. 

Octave,  214. 

Ohm,  354. 

Ohm's  Law,  357. 

Oil  surface,  effect  on  water,  122. 

Opaque  bodies,  435,  478. 

Open  circuit,  347. 

Opera  glasses,  494. 

Optical  center  of  a  Ions,  466. 

Optical  disk,  444. 

Optical  instruments,  491-500. 

Optical  lantern,  495. 

Oscillation,  electrical,  341. 

of  pendulum,  90. 
Oscillator  electric  fan,  52. 
Osmose,  127. 
Osmotic  pressure,  127. 
Overtones,  218,  223. 
Overturning  a  body,  work  done  in,  86 

Parabolic  curve,  45. 
Parachute,  40. 
Parallel  circuits,  387. 

resistance  of,  389. 
Parallel  currents,  action  of,  393. 
Parallel  forces,  58-60,  82,  83. 
Parallel  grouping  of  cells,  359. 
Parallelogram  of  forces,  54. 
Pascal's  Law,  130. 
P.  D.,  326. 
Pencil,  of  light,  436. 
Pendulum,  89. 

conical,  191. 

energy  of,  72. 

Pendulum  method  of  combining  vi- 
brations, 229. 
Penumbra,  436. 
Period,  of  a  pendulum,  91. 
Periscope,  138. 
Petroleum  reining,  276. 
Phase  of  wave,  193. 
Phonograph,  234. 


542 


INDEX 


Photographs,  497-499. 

sent  by  wire,  502. 
Photometry,  Photometers,  440. 
Physical  change,  9,  266. 
Physics,  denned,  13. 
Pinhole  camera,  438. 
Pipe,  musical  instrument,  225. 
Pitch,  of  screw,  110. 

of  sound,  210,  212. 
Plane  lenses,  465. 
Plane  mirror,  445. 
Plante,  Gaston,  377. 
Plates,  vibration  of,  227. 
Plating  by  electricity,  375. 
Plumb  line,  81. 
Pneumatic  tools,  162. 
Points,  action  on  electrical  charges, 

325. 

Polariscope,  490. 
Polarity  of  magnets,  301. 
Polarization  of  cell,  348. 
Polarized  light,  488. 
Poles,  of  a  cell,  347. 

of  an  electromagnet,  367. 

of  a  magnet,  302. 
Porosity,  15.  * 

Positive  electricity,  320. 
Potential,  electrical,  326;  see  Differ- 
ence of  potential. 

fall  of,  386. 
Potential  energy,  70. 
Pound,  31. 
Poundal,  47. 
Power,  rate  of  work,  76. 
Power  or  effort,  97. 
Powers,  mechanical,  98. 
Pressure,  atmospheric,  166-177. 

electrical,  353. 

liquid,  129-141. 

of  gases,  177-180. 
Pressure  gauge,  180. 
Primary  coil,  398. 
Principal  focal  length,  450. 
Principal  focus,  449. 
Prism  binocular,  494. 
Prisms,  461,  464. 
Projectiles,  44. 
Proof  plane,  322. 
Properties  of  matter,  14-33. 
Pulley,  105. 
Pumps,  159,  182-184. 
Pyrometer,  416. 


Radiation  of  heat,  254. 
Radiations,  invisible,  506-518. 
Radio-activity,  515. 
Radiographs,  513. 
Radiometer,  255. 
Rainbow,  475. 
Range  of  projectile,  46. 
Rarefaction,  sound  wave,  196. 
Ray  of  light,  436,  443,  457,  485. 
Reaction,  51. 
Real  focus,  450. 
Real  image,  453,  454. 
Receiver  of  telephone,  418. 
Rectilinear  motion,  34. 
Reed,  224. 

Reflected  motion,  62. 
Reflection,  angle  of,  62. 

law  of,  62,  444. 

of  light,  443. 

of  radiant  heat,  256. 

of  sound,  200. 

total,  460. 

Refracting  angle  of  a  prism,  465. 
Refraction  of  light,  457-472. 

angle  of,  457. 

double,  489. 

index  of,  458. 

laws  of,  459. 
Relative  density,  149. 
Relay,  371. 
Reluctance,  406. 
Residual  discharge,  334. 
Resistance,  in  electricity,  353. 

internal,  357,  391. 

laws  of,  354. 

measurement  of,  386. 

of  circuits  in  series,  388. 

of  parallel  circuits,  389. 

table  for  copper  wire,  355. 

unit  of,  354. 

Resistance,  in  machines,  97. 
Resistance  box,  coils.  383. 
Resolution  of  forces,  56. 
Resonance,  electrical,  506. 
Resonance,  in  sound,  203. 

method  of  measuring  velocity 

sound,  205. 
Resonator,  204,  232. 
Resultant,  53,  60. 
Rheostat,  385. 
Ring  armature,  406. 
Riveting  hammer,  162. 


INDEX 


543 


Rods,  vibration  of,  226. 
Roller  bearings,  113. 
Rontgen  rays,  513. 
Rotary  pump,  183. 
Rotation,  57. 
Ruhmkorff  coil,  400. 
Rutherford,  Ernest,  516. 

Saturated  solution,  25. 
.Saturation  of  water  vapor,  270. 
Scale,  musical,  214. 

thermometric,  241. 
Screw,  109. 
Secondary  coil,  398. 
Seconds  pendulum,  92. 
Self-induction,  398. 
Semitone,  216. 
Sensitive  flames,  234. 
Series  dynamo,  408. 
Series  grouping  of  cells,  358. 
Shadows,  436. 
Sharp,  in  music,  217. 
Short-circuiting,  350. 
Shunt  circuit,  387. 
Shunt  dynamo,  408. 
Simple  harmonic  motion,  191. 
Siphon,  180. 
Siren,  212. 
Soap  bubbles,  122. 
Solar  spectrum,  474. 
Solenoid,  365. 

Solenoid  galvanometer,  381. 
Solidification,  268. 
Solids,  defined,  11. 

expansion  of,  259. 

fusion  of,  267. 

heat  conductivity  of,  248. 

sound  transmitted  by,  195,  200. 
Solution,  25. 
Sonometer,  221. 
Sound, 191-236. 

defined,  194. 

intensity  or  loudness  of,  210. 

interference  of,  203. 

pitch  of,  212. 

quality  of,  218. 

reflection  of,  200. 

resonance,  203. 

vransmission  of,  195,  200. 

valocity  of,  198. 

vibrations.  192,  196.  203,  221. 

waves,  196. 


Sounder,  telegraph,  371. 
South  pole  of  magnet,  302. 
Space  passed  over,  36. 
Spark,  electric,  337. 
Specific  gravity,  146,  149. 

table  of,  150. 

Specific  gravity  bottle,  152. 
Specific  heat,  281. 
Specific  inductive  capacity,  330. 
Specific  properties,  14,  22. 
Spectroscope,  481. 
Spectrum,  474,  484. 

laws  of,  482. 
Spectrum,  normal,  487. 
Spectrum  analysis,  482. 
Speed,  36. 

Spherical  aberration,  455,  471. 
Spheroidal  state,  274. 
Stability,  85. 
Staff,  in  music,  214. 
Standards,  international,  30. 
Static  electricity,  318. 
Statics,  34. 
Steam,  284,  289. 
Steam  engine,  290. 

governor,  64. 
Steam  turbine,  292. 
Steelyard,  102. 
Storage  batteries,  376. 
Strain,  19. 
Stress,  19. 

Strings,  vibration  of,  221. 
Submarine,  136-138. 
Substances,  defined,  10. 
Substitution,  method  of,  102. 
Surface,  center  of  gravity  of,  82. 

unit  of,  31. 

Surface  of  a  liquid,  138. 
Surface  tension,  120. 
Sympathetic  vibrations,  206. 

Telegraph,  370. 

wireless,  507. 
Teleostereograph,  502. 
Telephone,  418. 
Telescope,  492. 
Temperament,  piano,  217. 
Temperature,  237. 

absolute,  265. 

critical,  276. 

measurement  of,  239. 
Tempering,  25. 


544 


INDEX 


Tenacity,  22. 
Tension,  surface,  120. 
Theory,  13. 
Thermal  unit,  281. 
Thermoelectric  couple,  415. 
Thermometers,  240-245. 
Thermos  bottle,  250. 
Thermostat,  261. 
Three-color  process,  481. 
Three-wire   system   of   incandescent 

lighting,  427. 
Thunder,  343. 
Timbre,  218. 
Time,  unit  of,  32. 
Toepler-Holtz  machine,  335. 
Tone,  210. 

Tonic  sol  fa  system,  215. 
Torricelli,  Evangelista,  172. 
Total  reflection,  460. 
Trajectory,  46. 
Transformer,  427. 
Translation,  57. 
Translucent  bodies,  435. 
Transmission  of  electrical  enerry,  431. 
Transmitter,  telephone,  419. 
Transparent  bodies,  435,  47U. 
Transverse  vibrations,  192. 
Tubes,  vibration  of,  226. 
Tungsten  lamp,  425. 
Turbine,  steam,  292. 
Turbine  water  wheel,  140. 

Umbra,  436. 
Uniform  motion,  36. 
Units,  28-32,  47,  48,  74. 

Vacuum,  195. 

Vacuum  cleaner,  184. 

Vapor,  157,  275. 

Vapor  tension  of  water,  288. 

Vaporization,  269. 

heat  of,  284. 

Variation,  magnetic,  310  311. 
Vector  lines,  52. 
Velocities,  composition  of,  61. 
Velocity,  36. 
Ventilation,  253. 
Vertical,  81. 


Vibrations,  and  wave  motion,  192. 

combination  of,  228. 

forced,  207. 

of  pendulums,  90,  92. 

sound,  191,  206,  221,  224,  226,  227 

sympathetic,  206. 
Virtual  focus,  451. 
Virtual  image,  453. 
Volt,  356. 
Voltaic  cell,  347. 
Voltameter,  374. 
Voltmeter,  380. 
Volume,  unit  of,  31. 

Water,  compressiblity,  132. 

evaporation  of,  269. 

expansion  of,  262. 

maximum  density,  149. 

physical  states  of,  283. 

specific  gravity,  149. 
Water  equivalent,  283. 
Water  vapor,  pressure  of,  288. 
Water  waves,  194. 
Water  wheel,  turbine,  140. 
Watt,  77,  391. 
Wave  length,  193. 
Waves,  192-198. 
Weather,    indicated    by    barometer, 

174. 

Wedge,  109. 
Weighing,    method    of    substitution, 

102. 

Weight,  27,  81. 
Weight  or  resistance,  97. 
Weston  cell,  356. 
Wheatstone  bridge,  387. 
Wheel  and  axle,  103. 
Wimshurst  machine,  337. 
Wind  instruments,  224. 
Wire.  24;  table,  355. 
Wireless  telegraphy,  507. 
Work,  74,  287. 
Worm,  275. 

X-rays,  513. 
Yard,  standard,  29. 
Zero,  absolute,  264. 


360/0 


UNIVERSITY  OF  CALIFORNIA  LIBRARY 


